Add files using upload-large-folder tool

-9AzT4oBgHgl3EQf_f5A/content/2301.01948v1.pdf

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:33ce56f197bd5c331e0dbf38aca2dd93597e6b0bf4ed8a6b0d3f371ffeacf53b
+size 1527886

-9AzT4oBgHgl3EQf_f5A/vector_store/index.faiss

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:8e4db0944738dca8dbe85fa3533f56e285fbe267102de4fa8d0df262840f5991
+size 6029357

-9AzT4oBgHgl3EQf_f5A/vector_store/index.pkl

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:bf91db6e34569b72041f7b29ba26bd4f89dc5be0c36cb48e3d0b8c3a285d7756
+size 222831

.gitattributes

@@ -1235,3 +1235,102 @@ LtAyT4oBgHgl3EQfgPig/content/2301.00356v1.pdf filter=lfs diff=lfs merge=lfs -tex
 99A0T4oBgHgl3EQfO__U/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
 edFST4oBgHgl3EQfFzg4/content/2301.13719v1.pdf filter=lfs diff=lfs merge=lfs -text
 edFST4oBgHgl3EQfFzg4/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+iNE1T4oBgHgl3EQfMwPW/content/2301.02994v1.pdf filter=lfs diff=lfs merge=lfs -text
+oNAzT4oBgHgl3EQfqf3Z/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+9NE4T4oBgHgl3EQfdgy1/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+79FLT4oBgHgl3EQfAy4h/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+sdE3T4oBgHgl3EQfMwm8/content/2301.04377v1.pdf filter=lfs diff=lfs merge=lfs -text
+d9FIT4oBgHgl3EQfoiuQ/content/2301.11319v1.pdf filter=lfs diff=lfs merge=lfs -text
+WtAyT4oBgHgl3EQfWPdu/content/2301.00159v1.pdf filter=lfs diff=lfs merge=lfs -text
+KdE4T4oBgHgl3EQfiA17/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+VdAyT4oBgHgl3EQfhfjt/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+LtAyT4oBgHgl3EQfgPig/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+VdAyT4oBgHgl3EQfhfjt/content/2301.00380v1.pdf filter=lfs diff=lfs merge=lfs -text
+iNE0T4oBgHgl3EQfYAA8/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+BNE5T4oBgHgl3EQfTA98/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+TdE5T4oBgHgl3EQfAQ7r/content/2301.05378v1.pdf filter=lfs diff=lfs merge=lfs -text
+XtAzT4oBgHgl3EQfmf3D/content/2301.01565v1.pdf filter=lfs diff=lfs merge=lfs -text
+oNE5T4oBgHgl3EQfkA8i/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+oNFPT4oBgHgl3EQfKjR1/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+GNFLT4oBgHgl3EQfGi_B/content/2301.11993v1.pdf filter=lfs diff=lfs merge=lfs -text
+wtE0T4oBgHgl3EQf-QJD/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+GNFLT4oBgHgl3EQfGi_B/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+TdE5T4oBgHgl3EQfAQ7r/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+4tFKT4oBgHgl3EQfRy39/content/2301.11773v1.pdf filter=lfs diff=lfs merge=lfs -text
+BNE5T4oBgHgl3EQfTA98/content/2301.05533v1.pdf filter=lfs diff=lfs merge=lfs -text
+XtAzT4oBgHgl3EQfmf3D/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+DNAzT4oBgHgl3EQfTvz-/content/2301.01257v1.pdf filter=lfs diff=lfs merge=lfs -text
+DNAzT4oBgHgl3EQfTvz-/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+ptFRT4oBgHgl3EQfdjek/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+r9A0T4oBgHgl3EQfK__H/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+b9E5T4oBgHgl3EQfEg5T/content/2301.05414v1.pdf filter=lfs diff=lfs merge=lfs -text
+XtFJT4oBgHgl3EQf5y0l/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+XtFJT4oBgHgl3EQf5y0l/content/2301.11671v1.pdf filter=lfs diff=lfs merge=lfs -text
+WdFRT4oBgHgl3EQfMjc9/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+ydE0T4oBgHgl3EQf-wKD/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+sdE3T4oBgHgl3EQfMwm8/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+U9FIT4oBgHgl3EQfgSvJ/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+MNFQT4oBgHgl3EQfVDaQ/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+lNE3T4oBgHgl3EQf5wv2/content/2301.04785v1.pdf filter=lfs diff=lfs merge=lfs -text
+PdE4T4oBgHgl3EQf-Q54/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+MNFQT4oBgHgl3EQfVDaQ/content/2301.13299v1.pdf filter=lfs diff=lfs merge=lfs -text
+-9AzT4oBgHgl3EQf_f5A/content/2301.01948v1.pdf filter=lfs diff=lfs merge=lfs -text
+PdE4T4oBgHgl3EQf-Q54/content/2301.05362v1.pdf filter=lfs diff=lfs merge=lfs -text
+d9FIT4oBgHgl3EQfoiuQ/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+LtE3T4oBgHgl3EQfYQrP/content/2301.04487v1.pdf filter=lfs diff=lfs merge=lfs -text
+xdFPT4oBgHgl3EQfQTRV/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+xdFPT4oBgHgl3EQfQTRV/content/2301.13041v1.pdf filter=lfs diff=lfs merge=lfs -text
+stAzT4oBgHgl3EQf6f5B/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+Q9E5T4oBgHgl3EQfZg88/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+ydE0T4oBgHgl3EQf-wKD/content/2301.02818v1.pdf filter=lfs diff=lfs merge=lfs -text
+Q9E5T4oBgHgl3EQfZg88/content/2301.05581v1.pdf filter=lfs diff=lfs merge=lfs -text
+i9E2T4oBgHgl3EQfIAa1/content/2301.03675v1.pdf filter=lfs diff=lfs merge=lfs -text
+stAzT4oBgHgl3EQf6f5B/content/2301.01875v1.pdf filter=lfs diff=lfs merge=lfs -text
+f9AzT4oBgHgl3EQfavwP/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+ItE4T4oBgHgl3EQfIgwL/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+AdFLT4oBgHgl3EQfEy_H/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+xdAzT4oBgHgl3EQfCfp8/content/2301.00960v1.pdf filter=lfs diff=lfs merge=lfs -text
+ItE4T4oBgHgl3EQfIgwL/content/2301.04912v1.pdf filter=lfs diff=lfs merge=lfs -text
+lNE3T4oBgHgl3EQf5wv2/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+7tE4T4oBgHgl3EQf2g0r/content/2301.05298v1.pdf filter=lfs diff=lfs merge=lfs -text
+VtE5T4oBgHgl3EQfcA97/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+FdE3T4oBgHgl3EQfVwo4/content/2301.04462v1.pdf filter=lfs diff=lfs merge=lfs -text
+VtE5T4oBgHgl3EQfcA97/content/2301.05600v1.pdf filter=lfs diff=lfs merge=lfs -text
+QNA0T4oBgHgl3EQfDP_p/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+YNE1T4oBgHgl3EQfcATB/content/2301.03180v1.pdf filter=lfs diff=lfs merge=lfs -text
+xdAzT4oBgHgl3EQfCfp8/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+QNA0T4oBgHgl3EQfDP_p/content/2301.02002v1.pdf filter=lfs diff=lfs merge=lfs -text
+RtFRT4oBgHgl3EQf8ThG/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+RtFRT4oBgHgl3EQf8ThG/content/2301.13683v1.pdf filter=lfs diff=lfs merge=lfs -text
+C9E1T4oBgHgl3EQfWATV/content/2301.03110v1.pdf filter=lfs diff=lfs merge=lfs -text
+4tFKT4oBgHgl3EQfRy39/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+WtAyT4oBgHgl3EQfWPdu/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+CdFQT4oBgHgl3EQfOTbk/content/2301.13275v1.pdf filter=lfs diff=lfs merge=lfs -text
+b9E5T4oBgHgl3EQfEg5T/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+a9E0T4oBgHgl3EQf4gJ0/content/2301.02739v1.pdf filter=lfs diff=lfs merge=lfs -text
+LdAzT4oBgHgl3EQfkf0t/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+LtE3T4oBgHgl3EQfYQrP/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+-9AzT4oBgHgl3EQf_f5A/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+CdFQT4oBgHgl3EQfOTbk/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+7tE4T4oBgHgl3EQf2g0r/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+ytFQT4oBgHgl3EQfyTYb/content/2301.13408v1.pdf filter=lfs diff=lfs merge=lfs -text
+rdE1T4oBgHgl3EQfPwNi/content/2301.03031v1.pdf filter=lfs diff=lfs merge=lfs -text
+FdE3T4oBgHgl3EQfVwo4/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+q9AzT4oBgHgl3EQfrP2-/content/2301.01642v1.pdf filter=lfs diff=lfs merge=lfs -text
+EdE4T4oBgHgl3EQffQ16/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+rdE1T4oBgHgl3EQfPwNi/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+yNAzT4oBgHgl3EQfQvuD/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+ddFAT4oBgHgl3EQfYx31/content/2301.08542v1.pdf filter=lfs diff=lfs merge=lfs -text
+idE3T4oBgHgl3EQfIwmA/content/2301.04337v1.pdf filter=lfs diff=lfs merge=lfs -text
+t9AzT4oBgHgl3EQfr_3p/content/2301.01654v1.pdf filter=lfs diff=lfs merge=lfs -text
+JtE2T4oBgHgl3EQfAQZo/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+q9AzT4oBgHgl3EQfrP2-/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+SNE0T4oBgHgl3EQf1wKp/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+XNE4T4oBgHgl3EQfNQyg/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+5tFIT4oBgHgl3EQf8CtK/content/2301.11400v1.pdf filter=lfs diff=lfs merge=lfs -text
+SNE0T4oBgHgl3EQf1wKp/content/2301.02704v1.pdf filter=lfs diff=lfs merge=lfs -text
+59E0T4oBgHgl3EQfvwFr/content/2301.02622v1.pdf filter=lfs diff=lfs merge=lfs -text
+idE3T4oBgHgl3EQfIwmA/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
+9tFLT4oBgHgl3EQfCC72/content/2301.11974v1.pdf filter=lfs diff=lfs merge=lfs -text
+ENFRT4oBgHgl3EQfAze2/content/2301.13463v1.pdf filter=lfs diff=lfs merge=lfs -text
+YNE1T4oBgHgl3EQfcATB/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text

29AyT4oBgHgl3EQfb_di/vector_store/index.pkl

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:a5f25b190acff38a90579a1c04ea0a45033aea90fb4b6bce0eff1c1ac76f6358
+size 179867

2dE4T4oBgHgl3EQfzw3P/content/tmp_files/2301.05277v1.pdf.txt

@@ -0,0 +1,1361 @@
+arXiv:2301.05277v1  [cs.HC]  12 Jan 2023
+DriCon: On-device Just-in-Time Context
+Characterization for Unexpected Driving Events
+Debasree Das, Sandip Chakraborty, Bivas Mitra
+Department of Computer Science and Engineering, Indian Institute of Technology Kharagpur, INDIA 721302
+Email: {debasreedas1994, sandipchkraborty, bivasmitra}@gmail.com
+Abstract—Driving is a complex task carried out under the
+influence of diverse spatial objects and their temporal inter-
+actions. Therefore, a sudden fluctuation in driving behavior
+can be due to either a lack of driving skill or the effect of
+various on-road spatial factors such as pedestrian movements,
+peer vehicles’ actions, etc. Therefore, understanding the context
+behind a degraded driving behavior just-in-time is necessary
+to ensure on-road safety. In this paper, we develop a system
+called DriCon that exploits the information acquired from a
+dashboard-mounted edge-device to understand the context in
+terms of micro-events from a diverse set of on-road spatial
+factors and in-vehicle driving maneuvers taken. DriCon uses the
+live in-house testbed and the largest publicly available driving
+dataset to generate human interpretable explanations against the
+unexpected driving events. Also, it provides a better insight with
+an improved similarity of 80% over 50 hours of driving data
+than the existing driving behavior characterization techniques.
+Index Terms—Driving behavior, spatial events, context analysis
+I. INTRODUCTION
+With an increase in the traffic population, we witnessed
+a phenomenal rise in road accidents in the past few years.
+According to the World Health Organization (WHO) [1], the
+loss is not only limited to humans but affects the GDP of
+the country as well. The officially reported road crashes are
+inspected mostly based on the macro circumstances, such as
+the vehicle’s speed, the road’s situation, etc. Close inspection
+of those macro circumstances reveals a series of micro-events,
+which are responsible for such fatalities. For example, suppose
+a driver hit the road divider and faced an injury while driving
+on a non-congested road. From the macro perspective, we
+might presume it is due to the driver’s amateurish driving
+skill or the vehicle’s high speed. But, it is also possible that
+some unexpected obstacles (say, crossing pedestrians/animals)
+arrived at that moment out of sight. The driver deviated from
+his lane while decelerating to avoid colliding with them.
+Therefore, recording these micro-events are crucial in iden-
+tifying the reasoning behind such accidents. Such contextual
+information, or micro-events, thus, can help various stakehold-
+ers like car insurance or app-cab companies to analyze the on-
+road driving behavior of their drivers. Interestingly, an app-cab
+company can penalize or incentivize their drivers based on how
+they handle such context and take counter-measures to avoid
+accidents.
+A naive solution to extract the context information is
+to analyze the traffic videos. Notably, CCTV cameras [2]
+capture only static snapshots of the events concerning the
+Live Deployment Setup
+(a)
+Output of DriCon
+(b)
+The Preceding
+Vehicle Suddenly
+Braked and
+The Ego Vehicle
+Abruptly Stopped
+and
+Faced Severe
+Jerkiness
+Fig. 1: DriCon: Hardware components and a running instance
+when a vehicle faced severe jerks
+moving vehicles. Existing works [2], [3] use dash-cam videos
+along with IMU sensor data for manual or partly automated
+investigation of the accident. Note that, human intervention is
+error-prone and labor-intensive with higher costs. The situation
+gets further complicated when multiple events are responsible
+for the accident. For instance, suppose the preceding vehicle
+suddenly brakes to avoid collision with a pedestrian or at
+a run-yellow traffic signal. Consequently, the ego vehicle
+has to decelerate abruptly, resulting in a two-step chain of
+responsible events for the unexpected stop. Thus, identifying
+spatiotemporal interactions among traffic objects are crucial in
+characterizing the root cause behind such incidents.
+Importantly, understanding the contexts behind the degraded
+driving behavior on the fly is not trivial and poses multi-
+ple challenges. First, this involves continuous monitoring of
+the driving behavior of the driver as well as an exhaustive
+knowledge of various on-road spatial micro-events. Expensive
+vehicles use LiDAR, Radar etc., to sense the driver and
+the environment [4], [5]; however, app-cab companies are
+resistant to invest in such high-end vehicles due to low-profit
+margin. Second, depending on the driving maneuvers taken,
+temporally interlinking the micro-events based on the vehicle’s
+interaction with on-road spatial objects is a significant research
+challenge. For example, if adverse snowy weather is observed
+on one day, its effect on traffic movements may last till the
+next day. In contrast, reckless driving would impact only a few
+other vehicles around and will not be temporally significant
+after a few minutes. Such temporal impacts of an event
+would vary depending on the type and space of the event.
+Third, spatial positions of the surrounding objects impact the
+driving maneuver. Precisely, along with temporal dependency,
+the distance between the ego vehicle and the surrounding
+
+objects plays a vital role. For example, a far-sighted pedestrian
+might cross the road at high speed, keeping a safe distance,
+but it is fatal if the distance to the vehicle is low. Existing
+literature [6], [7] have attempted to identify risky driving,
+e.g., vehicle-pedestrian interaction, through IMU and video
+analysis; however, they fail to capture such temporal scaling
+or the spatial dependency among surrounding objects. Fourth,
+identifying the context in real-time over an edge-device (such
+as a dashcam) is essential for providing a just-in-time feed-
+back. But, deploying such a system for context characterization
+and analysis from multi-modal data over resource-constrained
+edge-device is not straightforward.
+To address these challenges, we propose DriCon that
+develops
+a
+smart
+dash-cam
+mounted
+on
+the
+vehicle’s
+dashboard to characterize the micro-events to provide just-in-
+time contextual feedback to the driver and other stakeholders
+(like the cab companies). It senses the maneuvers taken by
+the ego vehicle through IMU and GPS sensors. In addition, a
+front camera mounted on the device itself, is used to analyze
+the relationship between various on-road micro-events and the
+driving maneuvers taken. This facilitates the system to run in
+each vehicle in a silo and makes it low-cost and lightweight.
+Fig. 1 shows a snapshot of the hardware components of
+our system mounted on a vehicle, and an example scenario
+where DriCon generates a live contextual explanation behind
+a sudden jerk observed in the vehicle. In summary, our
+contributions to this paper are as follows.
+(1) Pilot Study to Motivate Micro-Event Characterization:
+We perform a set of pilot studies over the Berkeley Deep
+Drive (BDD) dataset [8], the largest public driving dataset
+available on the Internet (as of January 16, 2023), to
+investigate the variations in driving behavior depending on
+various road types, time of the day, day of the week, etc.,
+and highlight the spatiotemporal micro-events causing abrupt
+changes in driving maneuvers.
+(2) Designing a Human Explainable Lightweight Causal
+Model: The development of DriCon relies on the (i) IMU
+& GPS data to infer the driving maneuvers, and (ii) object
+detection model & perspective transformation [9] to detect the
+surrounding objects and their actions to capture various spatial
+micro-events. Subsequently, we identify the spatiotemporal
+contexts whenever the driving behavior deteriorates during a
+trip. Finally, we implement Self Organizing Maps (SOMs),
+a lightweight but effective causal model to capture the
+spatiotemporal dependency among features to learn the
+context and generate human-interpretable explanations.
+(3)
+Deployment
+on
+the
+Edge: We deploy the whole
+architecture of DriCon on a Raspberry Pi 3 model, embedded
+with a front camera, IMU and GPS sensors (Fig. 1). For this
+purpose, we make both the IMU and visual processing of
+the data lightweight and delay-intolerant. Following this, the
+pre-trained model generates recommendations based on the
+ongoing driving trip and makes it efficient to run live for
+just-in-time causal inferences.
+(4) Evaluating DriCon on a Live System Deployment and
+with BDD Dataset: We evaluate DriCon on our live in-house
+deployment, as well as on the BDD dataset [8] (over the
+annotated data [10]), comprising 33 hours and 17 hours of
+driving, respectively. We obtain on average 70% and 80%
+similarity between the derived and the ground-truth causal
+features, respectively, with top-3 and top-5 features returned
+by the model, in correctly identifying the micro-events causing
+a change in the driving behavior. Notably, in most cases,
+we observe a good causal relationship (in terms of average
+treatment effect) between the derived features and the observed
+driving behavior. In addition, we perform different studies of
+the resource consumption benchmarks on the edge-device to
+get better insights into the proposed model.
+II. RELATED WORK
+Several works have been proposed in the literature on
+understanding road traffic and its implications for road fa-
+talities. Early research focused on traffic surveillance-based
+techniques to prevent road accidents. For instance, National
+Highway Traffic Safety Administration (NHTSA) [3] had
+recorded statistics about fatal accident cases; TUAT [2] has
+been collecting video records from taxis and drivers’ facial
+images since 2005 to derive injury instances into several
+classes along with driving behavior estimation. In India, the
+source of information behind the causes of traffic injuries is the
+local traffic police [11]. In contrast, works like [12], [13] learn
+the crime type and aviator mobility pattern just-in-time from
+street view images and raw trajectory streams, respectively.
+Apart from harnessing videos and crowd-sourced information,
+several works [14], [15] are done on abnormal driving behavior
+detection by exploiting IMU and GPS data. To prevent fatal
+accidents, authors [16]–[18] try to alert the drivers whenever
+risky driving signature is observed, such as lane departure or
+sudden slow-down indicating congestion. However, they have
+not looked into the effect of neighboring vehicles or other
+surrounding factors on various driving maneuvers.
+Interaction among the ego vehicle and other obstacles,
+such as pedestrians, adverse weather in complex city traffic,
+often affects the vehicle’s motion, consequently affecting
+the driving behavior. Existing studies [19] reveal that road
+category, unsignalized crosswalks, and vehicle speed often
+lead to a disagreement among pedestrians to cross the road,
+leading to road fatalities. A more detailed study [20], [21]
+focuses on causality analysis for autonomous driving, faces
+infeasibility in real-time deployment. Moreover, they only use
+a limited set of driving maneuvers, e.g., speed change only.
+Particularly, causal inferencing is challenging due to high
+variance in driving data and spurious correlation [22] between
+traffic objects and maneuvers. The existing works limit their
+study by considering only static road attributes or relying
+on single or multi-modalities from a connected road network
+system. Such methodologies will not be applicable for a
+single vehicle in real-time deployment unless connected to the
+
+system. In contrast, leveraging multi-modalities from onboard
+vehicle sensors can efficiently characterize the continuous
+and dynamic contexts behind unexpected driving behavior
+fluctuations. DriCon develops a system in this direction.
+III. MOTIVATION
+In an ideal scenario, two vehicles are likely to follow similar
+maneuvers under the same driving environment; but this is
+not the case in reality. Driving behavior varies according
+to the driver’s unique skill set and is influenced by the
+impact of various on-road events, such as the movement
+of other heavy and light vehicles, movement of pedestrians,
+road congestion, maneuvers taken by the preceding vehicle,
+etc., which we call spatial micro-events or micro-events, in
+short. In this section, we perform a set of pilot studies to
+answer the following questions. (a) Does a driver’s driving
+behavior exhibit spatiotemporal variations? (b) Do all
+micro-events occurrences during a trip similarly impact the
+driving behavior? (c) Does a sequence of inter-dependent
+micro-events collectively influence the driving behavior?
+Following this, we analyze the publicly-available open-source
+driving dataset named Berkeley Deep Drive dataset (BDD) [8]
+to answer these questions stating the impact of different micro-
+events on the driving behavior. The dataset contains 100k
+trips crowd-sourced by 10k voluntary drivers over 18 cities
+across two nations – the USA and Israel. The dataset has been
+annotated with a driving score on the Likert scale of 1 (worst
+driving) to 5 (best driving) for each 5-second of driving trips.
+A. Variation in Driving Behavior over Space and Time
+We first check whether the on-road driving behavior exhibits
+a spatiotemporal variation. For this purpose, we vary two
+parameters – road type as the spatial parameter (say, “High-
+way”, “City Street”, “Residential”), and time of the day as
+the temporal one (say, “Daytime”, “Nighttime”, “Dawn/Dusk”)
+in the BDD dataset. In this pilot study, we form 9 groups
+with 30 trips each, in a total of 270, where the trips under
+a group are randomly picked from the BDD dataset. We plot
+the distribution of the driving scores over all the trips for each
+group. From Fig. 2(a), it is evident that the score distribution
+varies both (a) for a single type of road at different times of
+the day, and (b) for different types of road at any given time of
+the day (with p < 0.05 reflecting its statistical significance).
+In the following, we investigate the role played by various
+micro-events behind the variations in driving behavior.
+B. Role of Spatial Micro-events
+Next, we inspect whether various on-road micro-events,
+which are characterized by the movements of other spatial
+objects such as “cars”, “pedestrians”, “trucks”, “buses”, “mo-
+torcycles”, “bicycles”, etc., impact a driver’s driving behavior
+in the same way across different times of the day. We
+perform this study by handpicking 30 trips along with their
+annotated driving scores for both day and night time from
+the BDD dataset. We compute the volume (say, count) of
+spatial objects extracted using the existing object detection
+algorithm [23] from the video captured during the trip and
+take the average count of each object for a 5-second time
+window. Thus, for both daytime and nighttime, we get two
+time-series distributions, (a) the count of each on-road spatial
+object captured over the trip video during each time window,
+and (b) the annotated driving scores at those time windows.
+Next, we compute the Spearman’s Correlation Coefficient
+(SCC) among these two distributions for day time and night
+time, respectively. From Fig. 2(b), we infer that mostly all the
+on-road spatial objects adversely affect the driving behavior
+(depicting a negative correlation). Cars and pedestrians affect
+the driving score majorly during the daytime. Whereas, at
+night time, trucks and buses, along with the cars, impact the
+driving behavior because heavy vehicles such as trucks move
+primarily during the nighttime. However, the effect of light
+vehicles such as motorcycles and bicycles is insignificant due
+to the dedicated lanes for their movements. This observation
+is further extended to Fig. 2(c), where the same study is done
+for weekdays vs. weekends. We extracted the day of the week
+using already provided timestamps in the BDD dataset and
+clubbed 30 trips from Monday to Friday for weekdays and 30
+trips from Saturday to Sunday for the weekend. From Fig. 2(c),
+we observe that during the early days of the week, cars,
+pedestrians, and trucks adversely affect the driving behavior,
+whereas the impact is less during the weekend. Hence, we
+conclude that different on-road objects exert diverse temporal
+effects on the driving behavior.
+C. Micro-events Contributing to Sudden Driving Maneuver:
+Abrupt Stop as a Use-case
+Finally, we explore whether multiple inter-dependent micro-
+events can be responsible for a particular driving maneuver
+that might degrade the driving behavior. For this purpose,
+we choose abrupt stop as the maneuver, which we extract
+from the GPS and the IMU data (the situations when a
+stop creates a severe jerkiness [24]). We take 30 trips for
+each scenario, including daytime, nighttime, weekdays, and
+weekends. For each scenario, we extract the instances when
+an abrupt stop is taken and record the corresponding micro-
+events observed at those instances. Precisely, we extract the
+presence/absence of the following micro-events: red traffic
+signal, pedestrian movements, presence of heavy vehicles as
+truck & bus, light vehicles as motorcycle & bicycle, and the
+preceding vehicles’ braking action (as peer vehicle maneuver),
+using well-established methodologies [10], [23]. We compute
+the cumulative count of the presence of each micro-events and
+the number of abrupt stops taken over all the trips for the
+four scenarios mentioned above. From Fig. 2(d) and (e), we
+observe that the red traffic signal, the peer vehicle maneuvers,
+and heavy vehicles mostly cause an abrupt stop during the
+nighttime and on weekdays. Therefore, we argue that multiple
+on-road micro-events, such as the reckless movement of heavy
+vehicles at night, force even an excellent driver to slam on the
+brake and take an unsafe maneuver.
+
+Highway
+City Street
+Residential
+2.0
+2.5
+3.0
+3.5
+4.0
+4.5
+5.0
+Driving Score
+(a)
+Cars
+Pedestrians
+Truck
+Bus
+Motorcycle
+Bicycle
+−0.8
+−0.6
+−0.4
+−0.2
+0.0
+0.2
+0.4
+0.6
+Spearman's Correlation
+Day Time
+Night Time
+(b)
+Cars
+Pedestrians
+Truck
+Bus
+Motorcycle
+Bicycle
+−0.6
+−0.4
+−0.2
+0.0
+0.2
+Spearman's Correlation
+Week Day
+Weekend
+(c)
+Red
+Signal
+Pedestrians
+Heavy
+Vehicles
+Light
+Vehicles
+Peer
+Vehicle
+Action
+0
+10
+20
+30
+40
+50
+60
+70
+%age of Occurences
+Day Time
+Night Time
+(d)
+Red
+Signal
+Pedestrians
+Heavy
+Vehicles
+Light
+Vehicles
+Peer
+Vehicle
+Action
+0
+10
+20
+30
+40
+50
+%age of Occurences
+Week Day
+Weekend
+(e)
+Fig. 2: (a) Variation of Driving Behavior with respect to Road Type and Time of the Day, (b)-(c) Impact of Spatial Micro-events
+on the Driving Score at Different (i) Time of the Day, (ii) Day of the Week, (d)-(e) Contributing Factors Observed behind
+Abrupt Stop at Different (i) Time of the Day, (ii) Day of the Week
+IV. PROBLEM STATEMENT AND SYSTEM OVERVIEW
+A. Problem Statement
+Consider that FM denotes the set of driving maneuvers
+and FS be the set of spatial micro-events. Fi be the set
+of temporally-represented feature variables corresponding to
+the driving maneuvers taken and on-road spatial micro-events
+encountered during a trip i. Let Ri
+T be the driving score
+at time T during the trip i. We are interested in inspecting
+the events occurred, representing the feature values Fi, when
+|Ri
+T − ˆRi
+T −1| > ǫ (ǫ is a hyper-parameter, we set ǫ = 1),
+reflecting the fluctuations in driving behavior. Here, ˆRi
+T −1 =
+⌈mean([Ri
+1, Ri
+T −1])⌉ represents the mean driving behavior till
+T −1. The output of the system is a characterization of {Fi
+M,
+Fi
+S}, as to whether a fluctuation in the driving behavior is due
+to the driving maneuvers only (Fi
+M) or forced by the spatially
+causal micro-events (Fi
+S). Finally, we target to generate the
+explanations based on {Fi
+M, Fi
+S} to give feedback to the
+stakeholders for further analysis of the driving profile.
+B. Feature Selection
+Leveraging the existing literature [24], we identified a
+set of feature variables at timestamp T representing various
+driving maneuvers FM of the ego vehicle. These features
+are – Weaving (AW
+T ), Swerving (AS
+T ), Side-slipping (AL
+T ),
+Abrupt Stop (AQ
+T ), Sharp Turns (AU
+T ), and Severe Jerkiness
+(AJ
+T ). Similarly, we consider the following feature variables
+corresponding to the spatial micro-events FS – Relative Speed
+(ST ) and Distance (DT ) between the ego and the preceding
+vehicle, preceding vehicle’s Braking Action (BT), volume
+of the peer vehicles in front of the ego vehicle indicating
+Congestion in the road (CT ), Pedestrian (PT ), and it’s speed
+(QT ), Traffic light (LT ), Heavy vehicles: {Bus & Truck}
+(HT ), Type of the Road (GT ), and Weather condition (WT ).
+Note that, we empirically select these features based on the
+existing literature and observations from the dataset; additional
+features can also be incorporated in DriCon without losing its
+generality.
+We next broadly introduce our system architecture. DriCon
+captures IMU, GPS, and video data from a dashcam (say,
+an edge-device) and characterizes the context behind the
+improved/degraded driving behavior on the fly. The system
+comprises three components: (a) Data Preprocessing and
+Feature Extraction, (b) Detection of Improved/Degraded
+Driving Behavior, and (c) Identification of Possible Context
+(see Fig. 3).
+4
+Pedestrian Crossed and
+The Ego Vehicle Abruptly
+Stopped and Faced Severe
+Jerkiness.
+Inferred Features: Crossing
+Pedestrians, Severe
+Jerkiness, Abrupt Stops
+INPUT: IMU, GPS & Video
++
+Driving Maneuvers
+Spatial Micro-events
+2
+4
+4
+Detect Change
+in Driving
+Behavior 
+Capture Time-
+Series Dependency
+Among Features
+Output: Generated Explanations
+(a)
+(b)
+(c)
+(d)
+(e)
+Data Preprocessing and Feature Extraction
+Identification of Possible Context
+Model Output
+Model
+Construction
+Fig. 3: DriCon System Flow and Modeling Pipeline
+C. Data Preprocessing and Feature Extraction
+The collected IMU and GPS sensor data are prone to
+noise due to the earth’s gravitational force, signal attenuation,
+and atmospheric interference. Hence, we implement a low-
+pass filter to eliminate such noises from IMU and GPS to
+compute inertial features for the extraction of the driving
+maneuvers (FM). Next, we preprocess the video data before
+extracting on-road spatial micro-events and their actions (FS).
+We up/downsample the acquired videos to a resolution of
+960 × 540p, preserving the signal-to-noise ratio above 20 dB.
+1) Driving Maneuvers - FM: In order to generate the
+features corresponding to different driving maneuvers (FM),
+we extract the instances of Weaving (AW
+T ), Swerving (AS
+T ),
+Side-slipping (AL
+T ), Abrupt Stop (AQ
+T ), Sharp Turns (AU
+T ),
+and Severe Jerkiness (AJ
+T ) from the IMU data using standard
+accelerometry analysis [10], [24].
+2) Spatial Micro-events - FS: Next, we implement the
+state-of-the-art video data-based object detection algorithms
+and further fine-tune them based on our requirements, as
+developing vision-based algorithms is beyond the scope of our
+work. We leverage the YOLO-V3 [23] algorithm trained on
+the COCO dataset [25] to detect a subset of traffic objects such
+as Pedestrians, Cars, Buses, Trucks, and Traffic Lights (de-
+picted as FS). Next, we estimate the influence of pedestrians’
+interactions, the presence of heavy vehicles (buses & trucks),
+traffic light signal transitions (red, yellow & green), and the
+cars on the driving behavior of the ego vehicle. Next, we
+discard the detected objects which depict a confidence score
+
+troficintao.50o6
+treffieliehtzo5
+cor.
+0.90r0.680
+trotmcliehtr0.27Daytime
+Nightime
+Dawn/Dusk< 50% and bounding boxes of area < 10k, capturing the fact
+that the far-sighted traffic objects around the ego vehicle exert
+marginal impact compared to the near-sighted ones. Addition-
+ally, the traffic objects in the mid-way of the road, broadly
+visible from the driver’s dashboard, will be of more influence
+than the left or right lanes, as the ego vehicle will follow
+them immediately. Thus, we divide each of the frames into
+0.2:0.6:0.2 ratio along the horizontal axis, as left:middle:right
+lanes. Therefore, we keep the Pedestrians PT , Cars, Heavy
+Vehicles as {Buses & Trucks} HT , which have bounding
+box co-ordinates within the middle lane boundary, and Traffic
+Light Signal Transitions LT (Red, Yellow & Green) without
+the lane information as traffic lights are often positioned on
+the left and right lanes. Since our pilot study demonstrated
+that the pedestrians and peer vehicles’ action significantly
+impact the driving maneuvers of the ego vehicle, (a) we extract
+the Pedestrian Speed (QT ), as well as identify the crossing
+pedestrians in the mid-way, and (b) we compute the preceding
+vehicle’s Braking Action (BT ), and Congestion (CT), as
+well as detect the Relative Speed (ST ) and Distance (DT )
+variation among the ego and the preceding vehicle. We apply
+perspective transformation and deep learning methods [9], [26]
+to infer the above. Finally, the above pipeline runs on each
+frame where the video is re-sampled to 15 frames-per-second.
+D. Detection of Driving Behavior Fluctuations
+The crux of DriCon is to capture the temporal dependency
+of various driving maneuvers and spatial micro-events when
+a change in the driving behavior is observed during the trip.
+For a run-time annotation of the driving behavior, we use an
+existing study [10] that provides a driving behavior score on
+the Likert scale [1 − 5] by analyzing driving maneuvers and
+other surrounding factors. We divide the trip into continuous
+non-overlapping time windows of size δ and compute the
+driving score at the end of every window U (denoted as RP
+U ),
+using the feature values captured during that window [10].
+To quantitatively monitor whether there is a change in the
+driving behavior during a window U, we compare RP
+U and
+ˆRP
+U =
+1
+U−1
+U−1
+�
+i=1
+RP
+i (mean driving score during previous U−1
+windows). Suppose this difference is significant (greater than
+some predefined threshold ǫ). In that case, DriCon proceeds
+towards analyzing the temporal dependency among the feature
+vectors at different time windows to understand the reason
+behind this difference.
+E. Identification of Possible Context
+In the final module, we use the feature vectors at different
+windows to build the model that identifies which features
+(FGEN) are responsible for the change in driving behavior
+during the window U. The model reactively seeks explanations
+behind such fluctuations by analyzing the effect of the micro-
+events that occurred over the past windows [1, · · · , (U − 1)]
+and the present window U. Finally, natural language-based
+human interpretable explanations are generated and fed back
+to the stakeholders for further analysis.
+V. MODEL DEVELOPMENT
+To develop the core model for DriCon, we leverage the
+already extracted features F ∈ {FM
+� FS} (details in §IV-C)
+to capture the temporal dependency of the past as well as the
+present events. In addition, DriCon derives the explanation be-
+hind the detected events through explanatory features FGEN.
+For this purpose, we need a self-explanatory model that
+can capture the spatiotemporal dependency among different
+driving maneuvers and micro-events associated with the on-
+road driving behavior. We choose a Self Organizing Map
+(SOM) [27] for constructing the model that can exploit such
+spatiotemporal dependencies with minimum data availability.
+The major limitation of the classical deep learning models
+(such as CNN or RNN) stems from the fact that, (i) deep
+networks consume heavy resources (say, memory), as well as
+suffer from huge data dependency, and (ii) they act as a black
+box, hence fail to generate human interpretable explanations
+behind certain predictions [28]. On the other hand, SOM is
+able to characterize the micro-events in runtime using feature
+variability and unlabelled data.
+Neighboring Radius
+F1
+F2
+F3
+FU
+Input
+Layer
+Learning Phase
+Feature
+Input
+Converge
+Final Map
+Code Book
+BMU
+Weight
+(a)
+(b)
+(c)
+No Change
+Change
+Fig. 4: Working Principle of SOM
+A. Inferring Explanatory Features using SOM
+The key idea behind obtaining the explanatory features is
+first to discover the spatiotemporal feature dependency. In
+DriCon, we derive so using Kohonen’s Self Organizing Map
+(see Fig. 4), as it is an unsupervised ANN-based technique
+leveraging competitive learning methods. Since DriCon runs
+on an edge-device, we employ a minimal number of model
+parameters to expedite the processing without compromising
+the performance. Precisely, we implement the codebook with
+147 neurons, spread out over a two-dimensional array of
+size 7 × 21 (where 7 is a hyperparameter depending on the
+maximum influence of the past windows during a trip, 21 cor-
+responds to the number of features in the feature space). These
+neurons are initialized with a random weight (see Fig. 4(a)),
+where the weight vector has the same length (of 21) as the
+feature vector. Next, we represent each trip with a 2D grid of
+size 8 × 21 (considering 8 consecutive windows in a trip) to
+capture the influence of the past windows [1, · · · , (U −1)] and
+the present window U. In principle, the inherent topological
+ordering of SOM groups the similar feature space (in windows
+[1, · · · , (U −1)]) into a single group, when there is no change
+in the driving behavior. On the contrary, the dissimilar ones
+
+(say, during the window U), when there exists a change in
+the driving behavior, are mapped into a different group, as
+depicted in Fig. 4(b,c).
+For instance, suppose on a trip, the ego vehicle abruptly
+stops due to the preceding vehicle’s braking action following
+a sudden change in the traffic signal. Hence the feature space
+in window [1, · · · , (U − 1)] exhibits a similar signature (until
+the abrupt stop occurs), and subsequently gets mapped to a
+single neuron. However, during the abrupt stop, there will be
+changes in the feature space (say, maneuvers and other spatial
+events). These changes in the feature space will get it assigned
+to a different neuron and settle the other neurons’ weight
+automatically depending on the changes in the feature space
+between the windows [1, · · · , (U −1)] and the window U. This
+procedure allows SOM to harness the temporal dependency
+among spatial events in an unsupervised mode, without using
+the driving score explicitly.
+1) Model Training: The input trip data is represented in
+the 2D grid format for learning the best-matched neuron,
+optimizing the Euclidean distance between the feature space
+and weight vector of the corresponding neuron. To ensure the
+best-fitting, the best-matched neuron tries to learn the weight
+vector of the feature space at most. Also, the neurons in the
+neighborhood try to tune their weights as nearest as possible
+compared to the best-matched neuron. We train this model
+for 500 epochs, where each neuron gets mapped with the
+best matching trip instances and converges to their coordinate
+position in the codebook. We implement the Bubble neigh-
+borhood function [29] to update the neighborhood neurons’
+weights until the neighborhood radius converges to ≈ 0. We
+ensure that both the distance and neighborhood functions are
+computationally faster for accurate learning accelerating the
+convergence. Upon completing the total number of epochs, we
+obtain the converged codebook called the Map, where each trip
+instance gets assigned to the best matching neuron called the
+Best Matching Unit (BMU). The weight vector corresponding
+to the BMU’s coordinate reveals the explanatory features
+FGEN.
+2) Model Execution: We leverage the constructed Map for
+the runtime inference. First, we conduct the feature processing
+of the current ongoing trip (following §IV-C), and in parallel,
+the extracted feature space is fed as input to the constructed
+Map. Eventually, we obtain the BMU’s coordinate and extract
+its corresponding weight vector and the feature encoding for
+the given trip instance. From the weight vector, we extract
+the top-k weights and their corresponding feature names
+(say, weather type) and their encoded values (say, weather
+type: rainy). Finally, we populate them in FGEN (called
+the Generative micro-events) for further generation of human
+interpretable explanation.
+B. Generating Textual Explanation
+DriCon aims to generate the explanations in textual format
+utilizing the output features FGEN for better readability and
+human interpretation. As the features f ∈ FGEN are already
+associated with some keywords (say, severe jerkiness), we
+need to generate them in a sentential form, keeping the features
+as “action” or “subject” depending on whether f ∈ FM
+or f ∈ FS, respectively. For instance, if the feature is an
+action, we assign the ego vehicle as the subject, replace the
+corresponding output feature f with its describing keyword,
+and finally concatenate them to obtain the sentential form.
+For example, in case of severe jerkiness, the constructed
+sentence becomes, “the ego vehicle severe jerks”. However, if
+the output feature f represents a subject, then many possible
+sentences can be generated out of one subject. Thus, we
+mine several traffic guidelines [30] and compute the cosine
+similarity among the features and existing guidelines using TF-
+IDF vectorizer. Upon extracting the most relevant guidelines,
+we fetch the object associated with the sentence and construct
+a single sentence for each output feature (e.g., “pedestrian
+crossing” → “pedestrian crossing the intersection”). Next, for
+all the generated sentences, the describing keywords corre-
+sponding to each feature are converted to an adjective or
+adverb using Glove [31] for better structuring of the sentences
+(say, “the ego vehicle severe jerks” → “the ego vehicle severely
+jerks”). Finally, each sentence is concatenated using the “and”
+conjunction, and repetitive subjects are replaced using their
+pronoun form using string manipulation to generate the whole
+explanation, as depicted in Fig. 3(e).
+VI. PERFORMANCE EVALUATION
+This section gives the details of DriCon implemented over
+a live setup as well as over the BDD dataset. We report the
+performance of the SOM model and compare it against a
+well-established baseline. Additionally, we show how well our
+system has generated the textual explanations along with a
+sensitivity analysis to distinguish how error-prone DriCon is.
+We start with the experimental setup details as follows.
+A. Experimental Setup
+DriCon is implemented over a Raspberry Pi 3 Model B
+microprocessor kit operating Raspbian OS with Linux kernel
+version 5.15.65 − v7+ along with 1 GB primary memory
+and ARMv7 processor. We primarily utilize the IMU, the
+GPS, and the video data captured through the front camera
+(facing towards the front windscreen) as different modalities.
+For this purpose, we embed one MPU−9250 IMU sensor,
+one u-blox NEO−6M GPS module, and one Logitech USB
+camera over the Raspberry Pi board, as depicted in Fig. 1(a).
+We deployed DriCon over three different types of vehicles
+(e.g., SUV, Sedan, & Hatchback). We hired 6 different drivers
+in the age group of [20 − 45] who regularly drive in practice.
+Therefore, our whole experimentation ran for more than two
+months over three cities, resulting in approximately 33 hours
+of driving over 1000 km distance. The drivers drove freely
+without any specific instructions given, with each trip varying
+from approximately 20 minutes to 2 hours. In addition, each
+driver drove over five different types of roads (city street,
+highway, residential, parking & campus road) at three different
+times of the day (day, dusk & night). We evaluate DriCon by
+analyzing how well our proposed model extracts the generative
+
+micro-events FGEN (see §V-B). For implementing DriCon,
+we consider δ = 5 seconds, ǫ = 1. The impact of other hy-
+perparameters and resource consumption have been discussed
+later during the analysis. We next discuss the ground-truth
+annotation procedure used for the evaluation of DriCon.
+B. Annotating Micro-events
+We launched an annotation drive by floating a Google
+form among a set of recruited annotators, where they had
+to watch a video of at most 10 seconds and choose the
+top-3 most influential factors impacting the driving behavior.
+We do this annotation over the in-house data (video data
+collected during the live experiments) and the videos over the
+BDD dataset. For each video from both the datasets given
+in the form, we showed only the clipped portion where the
+score fluctuations had occurred. Next, out of the total 15
+factors (including driving maneuvers and spatial micro-events)
+given in a list, they were instructed to choose the top-3 most
+influential factors responsible for the poor driving behavior
+based on their visual perception. Besides, we also provided
+the model-generated sentences (§V-B) and asked how relevant
+and well-structured the sentences are (on a scale of [1−5]) for
+explaining the change in the driving behavior. The annotators
+also had the option to write their own explanation if they
+perceived a better reason behind the driving behavior change.
+As the number of trips is quite large, we need to design a set
+of Google forms (sample form1), each containing at most 20
+videos to ensure the least cognitive load on the annotators. We
+also collected annotators’ demographic information such as
+age, gender, city, etc. We find that most participants (> 67%)
+had prior driving skills. At least three independent annotators
+had annotated each instance. Upon receiving the annotated
+factors, we need to find the agreement among the annotators
+to ensure the received ground truth is unbiased and non-
+random. As standard inter-annotator agreement policies (say,
+Cohen’s kappa index) work on quantitative analysis or one-to-
+one mapping, we cannot apply such metrics. Thus, we use the
+majority voting technique where each listed factor is assigned
+a percentage, signifying how many times the annotators choose
+that factor. Each factor having a vote of at least 60% is kept in
+FGT . We observe the minimum and the maximum cardinality
+of FGT are 3 and 5, respectively. This also indicates that
+the annotators agreed on selecting the factors that influenced
+the driving behavior. FGT contains the annotated micro-events
+against which FGEN is evaluated.
+C. Performance Metric
+We use the Dice Similarity Coefficient score [32] (N)
+which computes the similarity between FGT and FGEN as fol-
+lows: N = 2×|FGT ∩FGEN|
+|FGT |+|FGEN| . We report the mean N across all
+the trips to measure the accuracy of DriCon. Next, we also use
+Average Treatment Effect [33] (ATE) to report comparatively
+higher causal features out of the model identified features.
+Finally, we define Percentage of Error as follows. First, we
+1https://forms.gle/97N6uk4ujRaZSWbj8 (Accessed: January 16, 2023)
+Top-3
+Top-5
+30
+50
+70
+90
+Dice Coefficient (in %)
+(a)
+Top-3
+Top-5
+10
+30
+50
+70
+90
+Dice Coefficient (in %)
+(b)
+Fig. 5: (a) Dice Coefficient Similarity (in %) between Human
+Annotated and Model Generated Features (b) Ablation Study
+compute the set-difference as {FGT \FGEN}, and extract the
+corresponding feature category (say, FM, FS). Once we get
+the count of each feature category, we compute its percentage
+out of the total trips as the Percentage of Error.
+D. Baseline Implementation
+As a baseline for extracting FGEN, we implement a super-
+vised rule-based Random Forest (RF) algorithm with 20 deci-
+sion trees where each tree is expanded to an unlimited depth
+over the training data. We optimize the labels RP
+U with the
+intuition that features will contribute differently to each of the
+predicted scores. Although the RF-based model has a feature
+importance score signifying the contribution of each feature
+in constructing the model, we need to have an explanation of
+how each feature contributes to predicting the driving scores
+on a trip instance basis. Therefore, we use LIME [34] in the
+background of the RF model for generating the explanatory
+features. As LIME is a model-agnostic method, it tries to map
+the relationship between the input features and output scores
+by tweaking the feature values. Thus, it explains the range
+of values and probability for each feature that contributes
+to predicting the score. From the generated explanation, we
+extract the contributing features FGEN along with their values
+for further generation of textual explanation. This pipeline is
+executed in a similar manner as described in §VI-A.
+E. Accuracy of Characterized Context
+We present the accuracy of DriCon using the SOM and
+RF+LIME model over the in-house dataset using Dice Coeffi-
+cient Similarity N. We extract the top-k features from FGEN
+where k ∈ {3, 5} and compute N between the two sets of fea-
+tures – FGEN and FGT with top-k. Fig. 5(a) shows the result.
+For top-3, we get 69% & 40% similarity on average with SOM
+and RF+LIME, respectively. Whereas for top-5, we observe
+79% & 48% similarity on average with SOM and RF+LIME,
+respectively. As the in-house dataset has more complex micro-
+events, the slight performance drop over the in-house dataset
+using the top-3 features is tolerable. Intuitively, the model can
+capture more diversity as perceived by the human annotators;
+therefore, the similarity improves as we move from k = 3
+to k = 5. However, as the RF+LIME considers each time
+instance of a trip independently, its performance degrades.
+It captures the dominant features responsible for the driving
+behavior change within the current time window, contrary to
+inspecting past time windows’ impact.
+
+DriCon
+DriCon-man
+DriCon-spat.SOM
+RF WI LIMETABLE I: Similarity Measure among Human Annotated vs. Model Generated Output
+Instance#
+Human Annotated FGT
+Model Generated FGEN
+Similarity N(%)
+ATE
+1
+Poor Weather Conditions (Heavy Rainfall, Fog, etc.), Swerving,
+Congestion, Overtaking, Taking Abrupt Stop
+Congestion, Preceding Vehicle Braking,
+Weaving, Abrupt Stop, Severe Jerkiness
+40%
+1.96
+2
+Sideslip, Taking Abrupt Stop, Traffic Lights: Red
+Traffic Lights: Red, Congestion, Abrupt Stop
+66.67%
+2.5
+3
+Crossing Pedestrian, High Speed Variation among Cars, Weaving
+Severe Jerkiness, Crossing Pedestrian, Weaving
+66.67%
+1.35
+To have a glimpse, we present the explanatory features
+(FGEN) vs. human-annotated ones (FGT) in Table I for a
+sample of three test instances where the similarity (Dice coef-
+ficient) is comparatively lower. Interestingly, when there is a
+mismatch, we observe that the corresponding features from the
+model-generated and human-annotated ones are conceptually
+related for most of the time. Additionally, a positive high
+mean ATE value for the model-generated mismatched features
+signifies that the model perceived those features as more causal
+than normal human perception. It can be noted that an ATE
+value ≥ 1 indicates high causal relationships between the
+features and the corresponding effect (changes in the driving
+behavior). For example, in test instance #2, the mismatched
+features are Sideslip (for human generated) and Congestion
+(for model generated), where Congestion was relatively more
+causal, affecting the change in the driving behavior. By manu-
+ally analyzing this instance and interviewing the corresponding
+driver, we found that he indeed made a minor sideslip on a
+congested road. Indeed, the driver was not very comfortable
+in driving a manually-geared car on a congested road.
+2
+3
+4
+5
+Fig. 6: Generated Map from SOM for a 7×7 Network (Scaled
+Down)
+F. Ablation Study
+Next, we understand the importance of different feature
+categories corresponding to the driving maneuvers and on-road
+spatial events, as described in §IV-A, on the overall perfor-
+mance of DriCon. To study the impact of driving maneuvers
+and spatial features, we implement SOM, excluding each of
+the above feature classes one at a time, and evaluate N to
+inspect the importance of each. The two variants other than
+DriCon are constructed in the following way. (a) DriCon-
+man.: Here, we exclude the driving maneuvers FM and keep
+FS only. (b) DriCon-spat.: Next, we exclude the spatial
+features FS and keep FM only. We evaluate these two variants
+over both top-3 and top-5 generated features, along with
+DriCon containing all the features, as depicted in Fig. 5(b).
+On excluding the driving maneuvers and spatial features,
+performance drops to 45% and 31%, respectively, for top-5
+features. This drastic drop signifies the crucial importance of
+spatial features, as these are the frequently changing features
+responsible for fluctuating driving behavior.
+G. Model Insight
+To understand how the spatiotemporal dependency among
+different features corresponding to the driving maneuvers and
+various on-road spatial micro-events are derived, we use 49
+neurons spread over a 7 × 7 two-dimensional array (a smaller
+variant of the SOM network originally used to develop the
+model, as the original model having 147 neurons is difficult to
+visualize), fitted over 200 trips. This instance produces a Map
+as depicted in Fig. 6, where all the given trips are assigned
+to each of the neurons. The scores RP
+U are used only for
+visual depiction purpose of how the trips are located on the
+Map. Each trip captures the change in the driving behavior
+using the feature variation. The neurons with multi-color are
+of more importance than the mono-color, as in those, the
+score fluctuations are most observed. During a stand-alone
+trip, the features corresponding to each instance of the trip
+will have a similar value until there is a change in the driving
+behavior, thus getting assigned to the same neuron (mono-
+color). However, the difference in the driving behavior induces
+distinct feature values than the previous instances; thus, it gets
+assigned to a different neuron in the Map. The neurons having
+multi-color, as depicted in Fig. 6, map the trip instances where
+a sudden change of driving behavior has occurred.
+H. Dissecting DriCon
+We next benchmark the resource consumption behavior of
+DriCon, followed by an analysis of the model’s significance
+and sensitivity.
+1) Edge-device Resource Consumption: We benchmark
+the CPU & memory usage, processing time, temperature rise,
+and energy consumption over two cases: when (a) the device
+is idle, & (b) DriCon is running. From Fig. 7(a), we observe
+that in idle mode, on average, 2% of CPU (using “top”
+command) is used. In contrary, running DriCon acquires at
+most 10% of the processor, which is acceptable. However,
+the memory usage is a bit high (≈ 500MB) mainly due to
+video processing overhead as depicted in Fig. 7(b). Next,
+we show the required processing time starting from data
+acquisition to output generation on a number of trip basis.
+
+Idle
+Live
+2
+4
+6
+8
+10
+CPU Consumption (in %)
+(a)
+Idle
+Live
+100
+200
+300
+400
+500
+600
+Memory Consumption (in MB)
+(b)
+2.0
+2.5
+3.0
+3.5
+4.0
+4.5
+Processing Time (in mins)
+0
+5
+10
+15
+20
+25
+#Trips
+(c)
+Idle
+Live
+43
+46
+49
+52
+55
+58
+61
+Temperature Rise (in ∘ C)
+(d)
+0
+12
+24
+36
+48
+60
+Time (in mins)
+0
+5
+10
+15
+20
+25
+Energy Consumption (in W-Hr)
+Nexar
+Live
+Idle
+(e)
+Fig. 7: Resource Consumption over the Edge-device (a) CPU Usage (b) Memory Usage (c) Histogram of Processing Time
+w.r.t., #Trips (d) Temperature Rise, (e) Energy Consumed
+Relevance
+Well-Structured
+3
+4
+5
+Annotation Score
+(a)
+Spatial
+Maneuver
+0
+5
+10
+15
+%age of Error
+(b)
+Top-3
+Top-5
+30
+50
+70
+90
+Dice Coefficient (in %)
+(c)
+Fig. 8: (a) Significance of DriCon (b) Sensitivity Analysis of
+DriCon (c) Performance on BDD Dataset
+DriCon generates the output within ≈ 3 minutes only for
+majority of the trips, further validating shorter response time
+(see Fig. 7(c)). To further delve deeper, we also log the
+temperature hike (from “vcgencmd measure temp” command)
+and total energy consumption using Monsoon High Voltage
+Power Monitor [35] while running DriCon. From Fig. 7(d) &
+(e), we observe that the temperature hiked at most to 59°C,
+while on average, 13 Watt-hour energy is consumed, which is
+nominal for any live system. To benchmark DriCon, we have
+also measured the energy consumption of the Nexar dashcam,
+which consumes 22 Watt-hour on an average, while capturing
+very few driving maneuvers (say, hard brake) without any
+context. This further justifies that DriCon never exhausts the
+resources on the edge-device and is can accurately detect the
+micro-events precisely.
+2) Significance of Generated Explanation:
+Next, we
+check how significant our generated explanations are. As
+reported in §VI-B, we plot the distribution of annotated
+scores (given by the recruited annotators) for the two fields –
+“Relevance” and “Well-Structured”. “Relevance” signifies the
+generated explanation’s applicability in explaining unexpected
+events. In contrast, “Well-structured” indicates how well inter-
+pretative the generated sentences are as per human cognition.
+Fig. 8(a) depicts a median value of 5 and 4 for “Relevance”
+and “Well-Structured”, respectively, which further justifies
+the credibility of DriCon. We also compute the similarity
+between the human-annotated and model-generated sentences
+and obtain a minimum, maximum, and mean similarity value
+as 51.33%, 85.5% & 70.57%, respectively, using the TF-IDF
+vectorizer. Thus DriCon resembles human cognition level up
+to an indistinguishable level (between a human and model) of
+auto-generating a contextual explanation, which further shows
+its applicability to give feedback to the stakeholders for their
+decision-making procedure.
+3) Sensitivity of DriCon: Finally, we inspect the micro-
+events that DriCon fails to capture. Because, apart from a
+model’s efficiency, we must also look into its deficiency to
+analyze how much that might affect the overall performance.
+Especially, this is important in the case where stakeholders
+are boosting/penalizing the driver’s profile. As depicted in
+Fig. 8(b), incompetence to capture both the spatial and ma-
+neuvers is low. Although this might lead to degraded model
+performance, as studied in §VI-F; driving maneuvers (FM)
+do not contribute superiorly to model performance due to the
+inter-dependency on spatial features (FS). But for FS, the
+Percentage of Error is still ≤ 13%, making the system less
+sensitive into generating error-prone contextual explanations.
+I. Offline Performance
+Finally, we report the accuracy of our system over the BDD
+dataset comprising 17 hours of driving data over 1.5k trips
+using N. As depicted in Fig. 8(c), DriCon performs quite
+well on pre-recorded data, with N = {71%, 84%}, for top-
+3 and top-5 features. We observe that SOM can identify the
+micro-events in a better way for offline analysis with a public
+dataset. However, as running the system live is essential for a
+realistic driving environment other than offline analysis, this
+much of slight accuracy drop can be endured.
+VII. CONCLUSION
+This paper developed an intelligent system on the edge-
+device called DriCon leveraging multi-modalities to detect the
+micro-events responsible for unexpected fluctuations in driving
+behavior. The human-interpretable explanations generated by
+DriCon show their relevance and credibility in identifying
+such context. Further, the spatiotemporal dependency among
+various features is inspected in an unsupervised manner to
+capture a diverse set of driving scenarios. Additionally, the
+resource-friendly deployment over a live testbed further vali-
+dates DriCon. Although our study captures the context where
+each feature’s contribution is taken independently, inter-feature
+dependency is not captured explicitly. For instance, say, a
+driver suddenly weaves while taking a turn to avoid colliding
+with a crossing pedestrian, making the following vehicle’s
+driver slam the brake. Here, the first driver’s action is due
+to the crossing pedestrian, which in turn impacts the second
+driver’s action. The analysis of such complex and collective
+interactions among the vehicles needs a more sophisticated
+
+SOM
+RF W/ LIMEsystem, possibly a different modality that can connect the
+inter-vehicle interactions. However, DriCon provides a simple,
+in-the-silo solution that can be independently deployed over
+vehicles with a dashboard-mounted edge-device or dashcam.
+REFERENCES
+[1] “Road
+traffic
+injuries,
+by
+world
+health
+organization
+(who),”
+https://www.who.int/news-room/fact-sheets/detail/road-traffic-injuries,
+2022, (Online Accessed: January 16, 2023).
+[2] “Institute
+of
+engineering
+tokyo
+university
+of
+agriculture
+and
+technology
+(tuat).
+smart
+mobility
+research
+center
+-
+research.”
+https://web.tuat.ac.jp/∼smrc/research.html,
+2017,
+(Online
+Accessed:
+January 16, 2023).
+[3] N. H. T. S. A. (NHTSA)., https://www.nhtsa.gov/, (Online Accessed:
+January 16, 2023).
+[4] “Lidars
+for
+self-driving
+vehicles:
+a
+technological
+arms
+race,”
+https://www.automotiveworld.com/articles/lidars-for-self-driving-vehicles-a-technological-arms-race/,
+2020, (Online Accessed: January 16, 2023).
+[5] Z. Li, C. Wu, S. Wagner, J. C. Sturm, N. Verma, and K. Jamieson, “Reits:
+Reflective surface for intelligent transportation systems,” in 22nd ACM
+HotMobile, 2021, pp. 78–84.
+[6] R. Akikawa, A. Uchiyama, A. Hiromori, H. Yamaguchi, T. Higashino,
+M. Suzuki, Y. Hiehata, and T. Kitahara, “Smartphone-based risky traffic
+situation detection and classification,” in IEEE PerCom Workshops,
+2020, pp. 1–6.
+[7] D. A. Ridel, N. Deo, D. Wolf, and M. Trivedi, “Understanding
+pedestrian-vehicle interactions with vehicle mounted vision: An lstm
+model and empirical analysis,” in 2019 IEEE Intelligent Vehicles Sym-
+posium (IV), pp. 913–918.
+[8] F. Yu, W. Xian, Y. Chen, F. Liu, M. Liao, V. Madhavan, and T. Darrell,
+“Bdd100k: A diverse driving video database with scalable annotation
+tooling,” arXiv preprint arXiv:1805.04687, vol. 2, no. 5, p. 6, 2018.
+[9] “Vehicle
+detection
+and
+distance
+estimation,”
+https://towardsdatascience.com/vehicle-detection-and-distance-estimation-7acde48256e1,
+2017, (Online Accessed: January 16, 2023).
+[10] D. Das, S. Pargal, S. Chakraborty, and B. Mitra, “Dribe: on-road mobile
+telemetry for locality-neutral driving behavior annotation,” in 23rd IEEE
+MDM, 2022, pp. 159–168.
+[11] D.
+Mohan,
+G.
+Tiwari,
+and
+K. Bhalla,
+“Road
+safety
+in
+india:
+Status report 2019. new delhi: Transportation research & injury
+prevention
+programme,
+indian
+institute
+of
+technology
+delhi.”
+http://tripp.iitd.ac.in/assets/publication/Road Safety in India2018.pdf,
+2019, (Online Accessed: January 16, 2023).
+[12] K. Fu, Z. Chen, and C.-T. Lu, “Streetnet: preference learning with
+convolutional neural network on urban crime perception,” in Proceedings
+of the 26th ACM SIGSPATIAL, 2018, pp. 269–278.
+[13] K. Patroumpas, N. Pelekis, and Y. Theodoridis, “On-the-fly mobility
+event detection over aircraft trajectories,” in Proceedings of the 26th
+ACM SIGSPATIAL, 2018, pp. 259–268.
+[14] I. Janveja, A. Nambi, S. Bannur, S. Gupta, and V. Padmanabhan,
+“Insight: monitoring the state of the driver in low-light using smart-
+phones,” Proceedings of the ACM on Interactive, Mobile, Wearable and
+Ubiquitous Technologies, vol. 4, no. 3, pp. 1–29, 2020.
+[15] X. Fan, F. Wang, D. Song, Y. Lu, and J. Liu, “Gazmon: eye gazing
+enabled driving behavior monitoring and prediction,” IEEE Transactions
+on Mobile Computing, 2019.
+[16] M. Walch, M. Woide, K. M¨uhl, M. Baumann, and M. Weber, “Coop-
+erative overtaking: Overcoming automated vehicles’ obstructed sensor
+range via driver help,” in 11th ACM AutomotiveUI, 2019, pp. 144–155.
+[17] H. T. Lam, “A concise summary of spatial anomalies and its application
+in efficient real-time driving behaviour monitoring,” in Proceedings of
+the 24th ACM SIGSPATIAL, 2016, pp. 1–9.
+[18] S. Moosavi, B. Omidvar-Tehrani, R. B. Craig, A. Nandi, and R. Ram-
+nath, “Characterizing driving context from driver behavior,” in Proceed-
+ings of the 25th ACM SIGSPATIAL, 2017, pp. 1–4.
+[19] Y. Shi, R. Biswas, M. Noori, M. Kilberry, J. Oram, J. Mays, S. Kharude,
+D. Rao, and X. Chen, “Predicting road accident risk using geospatial
+data and machine learning (demo paper),” in Proceedings of the 29th
+ACM SIGSPATIAL, 2021, pp. 512–515.
+[20] M. R. Samsami, M. Bahari, S. Salehkaleybar, and A. Alahi, “Causal imi-
+tative model for autonomous driving,” arXiv preprint arXiv:2112.03908,
+2021.
+[21] V. Ramanishka, Y.-T. Chen, T. Misu, and K. Saenko, “Toward driving
+scene understanding: A dataset for learning driver behavior and causal
+reasoning,” in IEEE CVPR, 2018, pp. 7699–7707.
+[22] F. Codevilla, E. Santana, A. M. L´opez, and A. Gaidon, “Exploring the
+limitations of behavior cloning for autonomous driving,” in IEEE/CVF
+ICCV, 2019, pp. 9329–9338.
+[23] J. Redmon and A. Farhadi, “Yolov3: An incremental improvement,”
+arXiv, 2018.
+[24] J. Yu, Z. Chen, Y. Zhu, Y. Chen, L. Kong, and M. Li, “Fine-grained ab-
+normal driving behaviors detection and identification with smartphones,”
+IEEE Transactions on Mobile Computing, vol. 16, no. 8, pp. 2198–2212,
+2016.
+[25] T.-Y. Lin, M. Maire, S. Belongie, J. Hays, P. Perona, D. Ramanan,
+P. Doll´ar, and C. L. Zitnick, “Microsoft coco: Common objects in
+context,” in ECCV.
+Springer, 2014, pp. 740–755.
+[26] D. Das, S. Pargal, S. Chakraborty, and B. Mitra, “Why slammed
+the brakes on? auto-annotating driving behaviors from adaptive causal
+modeling,” in IEEE PerCom Workshops, pp. 587–592.
+[27] T. Kohonen, “The self-organizing map,” Proceedings of the IEEE,
+vol. 78, no. 9, pp. 1464–1480, 1990.
+[28] C. Rudin, “Stop explaining black box machine learning models for high
+stakes decisions and use interpretable models instead,” Nature Machine
+Intelligence, vol. 1, no. 5, pp. 206–215, 2019.
+[29] “Neighborhood function,” https://users.ics.aalto.fi/jhollmen/dippa/node21.html,
+(Online Accessed: January 16, 2023).
+[30] “Guidelines
+for
+pedestrian
+facilities,”
+http://www.irc.nic.in/admnis/admin/showimg.aspx?ID=345,
+(Online
+Accessed: January 16, 2023).
+[31] J. Pennington, R. Socher, and C. D. Manning, “Glove: Global vectors
+for word representation,” in EMNLP, 2014, pp. 1532–1543.
+[32] A. Carass, S. Roy, A. Gherman, J. C. Reinhold, A. Jesson, T. Arbel,
+O. Maier, H. Handels, M. Ghafoorian, B. Platel et al., “Evaluating
+white matter lesion segmentations with refined sørensen-dice analysis,”
+Scientific reports, vol. 10, no. 1, pp. 1–19, 2020.
+[33] D. B. Rubin, “Estimating causal effects of treatments in randomized and
+nonrandomized studies.” Journal of educational Psychology, vol. 66,
+no. 5, p. 688, 1974.
+[34] M. T. Ribeiro, S. Singh, and C. Guestrin, ““why should i trust you?”
+explaining the predictions of any classifier,” in Proceedings of the 22nd
+ACM SIGKDD, 2016, pp. 1135–1144.
+[35] “Monsoon
+high
+voltage
+power
+monitor,”
+https://www.msoon.com/online-store/High-Voltage-Power-Monitor-p90002590,
+(Online Accessed: January 16, 2023).
+

4dFAT4oBgHgl3EQfExzK/content/tmp_files/2301.08424v1.pdf.txt

@@ -0,0 +1,1016 @@
+Possible new phase transition in the 3D Ising Model
+associated with boundary percolation
+Michael Grady
+Department of Physics
+State University of New York at Fredonia
+Fredonia NY 14063 USA
+[email protected]
+January 23, 2023
+Abstract
+In the ordered phase of the 3D Ising model, minority spin clusters are surrounded by
+a boundary of dual plaquettes. As the temperature is raised, these spin clusters become
+more numerous, and it is found that eventually their boundaries undergo a percolation
+transition when about 13% of spins are minority. Boundary percolation differs from the
+more commonly studied site and link percolation, although it is related to an unusual
+type of site percolation that includes next to nearest neighbor relationships. Because
+the Ising model can be reformulated in terms of the domain boundaries alone, there is
+reason to believe boundary percolation should be relevant here. A symmetry-breaking
+order parameter is found in the dual theory, the 3D gauge Ising model. It is seen to
+undergo a phase transition at a coupling close to that predicted by duality from the
+boundary percolation. This transition lies in the disordered phase of the gauge theory
+and has the nature of a spin-glass transition.
+Its critical exponent ν ∼ 1.3 is seen
+to match the finite-size shift exponent of the percolation transition further cementing
+their connection. This predicts a very weak specific heat singularity with exponent
+α ∼ −1.9. The third energy cumulant fits well to the expected non-infinite critical
+behavior in a manner consistent with both the predicted exponent and critical point,
+indicating a true thermal phase transition. Unlike random boundary percolation, the
+Ising boundary percolation has two different ν exponents, one associated with largest-
+cluster scaling and the other with finite-size transition-point shift. This suggests there
+are two different correlation lengths present.
+PACS: 05.50+q, 05.70.Jk, 64.60.ah, 64.60.F
+Keywords: Ising model, Gauge Ising model, spin glass, percolation, phase transition
+arXiv:2301.08424v1  [cond-mat.stat-mech]  20 Jan 2023
+
+1
+Introduction
+The Ising models in two and three dimensions are the most basic spin models which undergo
+order-disorder transitions. These have been extremely well studied and, of course, an exact
+solution exists in the two-dimensional case. The 3D model has always been a bit more of a
+mystery, and in this paper we explore the possibility of a weak secondary phase transition
+within the ordered phase.
+Presumably this is associated with some geometrical change
+in spin-clustering, but the exact nature of this reordering is unknown. The situation is
+clearer in the dual theory, the 3D gauge Ising model. Here the suspected transition is in
+the disordered phase, and clearly has the nature of a spin-glass transition. In other words
+we have identified a symmetry-breaking order parameter in the dual theory, but not in
+the Ising model itself. However, the Ising model does exhibit an interesting percolation
+phenomenon near the critical point predicted by duality from the spin-glass transition.
+This is a percolation of the domain boundaries between + and - spin clusters. As shown
+below, boundary percolation can be considered a third type of percolation, beyond site and
+link percolation, although it has a close relationship to an unusual type of site percolation.
+Of course percolation is not always related to a phase transition, but sometimes it is.
+It’s linkage in this case to a symmetry-breaking transition in the dual theory provides
+strong evidence that it is associated with a phase transition in this case. The argument is
+further strengthened by independent fits of the third energy cumulant to consistent critical
+behavior about the suspected critical point. Each investigation, the order-parameter in the
+dual theory, the boundary percolation finite-size shift, and the third energy moment, yields
+an independent determination of the critical exponent ν, all of which agree to a fairly close
+tolerance.
+In the following, first the boundary percolation concept is fleshed out and studied in
+both the 2D and 3D Ising models, as well as for 3D random percolation. It is found that
+the latter has the same critical exponents as for site percolation, and in fact is equivalent to
+site percolation if next to nearest neighbors are included in the cluster definition. The 3D
+Ising case is particularly interesting in that an analysis of the finite-size shift in percolation
+threshold gives a critical exponent very different from the percolation value, even though
+the cluster scaling still obeys the percolation exponents. This suggests it is linked to a phase
+transition with its own dynamical scaling and correlation length. Then we move on to the
+dual theory and introduce the spin-glass order parameter. A Monte Carlo study here shows
+clear crossings in the Binder cumulant and second-moment correlation length divided by
+lattice size. Correlation-length finite-size scaling is exhibited around the suspected critical
+point using scaling collapse plots, which also yield critical exponents. The critical exponent
+ν is found to match well with that found from the finite-size shift in percolation threshold.
+Finally, we study energy moments, such as specific heat and higher moments. Unlike an
+order parameter, these have both critical and non-critical pieces, so fitting can be difficult.
+This leads to the selection of the third energy cumulant as the best prospect for finding
+critical behavior as it can be fit without a non-critical part other than a constant. A Monte
+Carlo study with several times 109 sweeps per point on 303, 403, and 503 lattices yields a
+precise determination of this quantity. An independent critical behavior fit in the region of
+the suspected critical point gives values for both ν and κc which agree well with the two
+2
+
+other predictions. A substantial jump in the coefficient of the critical scaling fit across the
+transition further cements evidence for a thermal singularity here.
+The rather high value of ν ∼ 1.3 gives a highly negative value for the specific heat
+exponent α = 2 − dν ∼ −1.9. This means that both the specific heat and third cumulant
+have finite singularities. A very weak infinite singularity is expected in the fourth cumulant
+and stronger ones in fifth and higher.
+In the Ehrenfest classification this transition is
+fourth order.
+We attempted to measure fourth and fifth cumulants to find evidence of
+peaks growing with lattice size as expected from infinite singularities, but even with the
+rather large sample size here, these were still largely obscured by random error. However,
+finite singularities are just as singular as infinite ones, so perhaps one lesson is that one
+should not necessarily obsess over trying to find infinite singularities in transitions of such
+high order.
+Figure 1: Example of a boundary cluster. Sites marked with dots have opposite orientation to all
+surrounding sites.
+3
+
+2
+Boundary percolation
+The standard partition function for the Ising model is
+Z =
+�
+{σ}
+exp(κ
+�
+n.n.
+σiσj),
+(1)
+where the σ’s are classical spins taking values ±1 and the coupling is between nearest
+neighbors only. There is a well-known reformulation of the Ising models in terms of the
+boundaries themselves[1]. This reformulation even leads to an alternate exact solution in
+the 2D case[2]. The partition function can be written
+Z =
+�
+A
+N(A) exp(−κA)
+(2)
+where A is the total area of dual boundary plaquettes (or dual boundary links in 2D) in
+a configuration and N(A) are the number of distinct non-intersecting boundary configura-
+tions with that area. In this formulation there are no spins or domains. Only the boundary
+surfaces need exist, and the entropy associated with these surfaces controls the phase tran-
+sition. This is one reason why percolation of the domain boundary might be important for
+this model, as opposed to, say, site percolation. For instance, the density of states could
+change abruptly when an infinite boundary cluster forms, because for a finite cluster the
+area is usually an increasing function of the volume, whereas an infinite cluster can easily
+grow in volume without adding much to the area. If this were the case then the free energy
+would form a singularity at the boundary percolation point.
+We define boundary percolation as follows. Consider the set of all boundary links that
+connect + and - sites.
+These are each associated with a plaquette on the dual lattice.
+These plaquettes form closed surfaces separating clusters of + and - spins. These surfaces
+can form clusters themselves, if we define boundary clusters to be made up of boundary
+surfaces that share dual-lattice links. For instance, Fig. 1 shows a single boundary cluster.
+This same configuration would, however, count as two separate site-clusters, since sites are
+clustered only along lattice directions. If the site cluster concept is extended to include
+sites connected by face diagonals, i.e next nearest neighbors (NNN) in addition to near-
+est neighbors (NN), then these redefined site clusters would appear to coincide with the
+boundary cluster concept. Indeed we have verified for thousands of configurations that
+those with percolating boundaries also have percolating NN+NNN site-clusters, and vice
+versa, so they do appear to measure the same thing.
+It seems boundary percolation, which in three dimensions could also be called plaquette
+percolation, has only been studied before in the form of the equivalent extended NN+NNN
+site percolation problem[3], as a part of surveys of various extended percolation models, but
+never applied to the Ising model. The main result of these studies is establishing a threshold
+for random NN+NNN percolation at a minority site probability of 0.1372(1). Because the
+Ising model is interacting, correlations would be expected to modify this result, but still
+it should be kept in mind.
+Fig. 2ab shows the evolution of the Ising model boundary
+percolation threshold κ∗
+L with lattice size L for both two and three dimensions. These both
+4
+
+scale well with the finite-size scaling relation
+κ∗
+L = κc − cL−1/ν
+(3)
+where κc is the infinite lattice threshold. The percolation threshold is defined here as the
+point where 50% of lattices have a cluster which percolates in all directions. For two dimen-
+sions, boundary percolation exists in the random phase, and ceases in the ferromagnetic
+phase. The above fit gives κc = 0.4405(5) which agrees well with the known ferromagnetic
+transition point 1
+2 ln(
+√
+2 + 1) ≃ 0.44069. This is just the opposite of majority-site perco-
+lation, which happens only in the magnetized phase. Thus in two dimensions boundary-
+percolation and site-percolation seem equally relevant.
+The exponent derived from the
+finite-size scaling fit to Fig. 2a is ν = 1.261(18). This seems slightly different from the
+standard 2D site-percolation exponent ν = 4/3 but of course that is for a non-interacting
+system. There could also be a small correction from next to leading order scaling effects.
+As far as we know, the critical exponents for random NN+NNN site percolation or ran-
+dom boundary-percolation have not been previously measured.
+In principle they could
+differ from site percolation, however in three dimensions we find below that the critical
+exponents for random boundary percolation appear to be the same as for ordinary site
+percolation. Probably the same is true in two dimensions, but we did not perform that
+measurement.
+0.37
+0.38
+0.39
+0.40
+0.41
+0.42
+0.43
+0.44
+0.45
+0.000
+0.005
+0.010
+0.015
+0.020
+0.025
+k*
+L
+1/L
+0.2475
+0.2480
+0.2485
+0.2490
+0.2495
+0.000
+0.005
+0.010
+0.015
+0.020
+0.025
+0.030
+k*
+L
+1/L
+Figure 2: Finite-size shift of the boundary percolation threshold for the 2D (a) and 3D (b) Ising
+model. Error bar ranges are 1/10 to 1/20 of symbol size.
+In two dimensions minority sites never percolate. In three dimensions there are a lot
+more paths. Majority sites always percolate and minority sites percolate in the random
+phase and about the first 5% of the ferromagnetic phase, measured by temperature. Even-
+tually minority sites get too few and percolation is lost at κ = 0.2346(13) where the mag-
+netization is about 0.62[4]. There is no visible effect on other quantities at this point. For
+comparison, the ferromagnetic transition is at κ = 0.2216595(26) [5]. Because in boundary
+5
+
+percolation the clusters are more liberally defined, it persists even further into the ferro-
+magnetic phase. From the fit to Fig. 2b we find κc = 0.24781(4) and ν = 1.30(3). Here the
+magnetization is about 0.7364. This means that 13.18(4)% of the sites are minority, which
+is about 4% lower than the value mentioned above, pc = 0.1372, for random NN+NNN site
+percolation (our study of random boundary percolation below also corroborates this value).
+The value found here for the exponent ν is particularly interesting. It is not at all close to
+the correlation length exponent for random site percolation ν ≃ 0.88[6, 7] measured from
+the finite-size scaling of the infinite cluster. For random boundary percolation we find a
+similar value below. Even in the 3D Ising case where interactions could change the result
+we still find scaling of the largest cluster gives ν ≃ 0.87 (detailed below). We are led to
+conclude that a different correlation length is controlling the finite-lattice shift exponent in
+this case. This makes the case of boundary percolation in the 3D Ising model of consider-
+able theoretical interest, because a system with two different correlation lengths diverging
+at the same place is, to say the least, unusual.
+0.1360
+0.1362
+0.1364
+0.1366
+0.1368
+0.1370
+0.1372
+0.1374
+0.000
+0.002
+0.004
+0.006
+0.008
+0.010
+p*
+L
+1/L
+Figure 3: Finite-size shift of boundary percolation threshold for 3D random percolation model.
+Error bar range is about 1/8 symbol size.
+Now we consider the case of random boundary percolation. This is an interaction-free
+model where positive sites are placed at random in the lattice, with the fraction of positive
+sites given as p. The remaining sites are, of course, set negative. Fig. 3 shows the finite-size
+shift of percolation threshold, p∗
+L. From the scaling relation given above we find the infinite
+lattice threshold as pc = 0.13730(4), which is fairly close to the percentage of positive sites
+at the 3D Ising boundary percolation threshold (they differ by 4%). However, the exponent
+here is quite different from the 3D Ising value of 1.30(3). We find ν = 0.91(5), consistent
+with well-known measurements of the site-percolation exponent. One can also determine ν
+from scaling of the largest cluster. If one defines P to be the fraction of plaquettes occupied
+by the largest cluster, then the same finite-size scaling analysis as is usually applied to the
+magnetization in a magnetic system undergoing a thermal phase transition can be applied
+[8] to P, its susceptibility
+6
+
+χ = (< P 2 > − < P >2)Np
+(4)
+and the corresponding Binder fourth-order cumulant
+U = (< P 4 > − < P 2 >2)/(3 < P 2 >2).
+(5)
+Here Np is the number of plaquettes in the lattice. The correlation-length scaling hypoth-
+esis implies that these should collapse onto universal functions if scaled according to their
+0.40
+0.45
+0.50
+0.55
+0.60
+0.65
+0.136
+0.137
+0.138
+0.139
+0.140
+U
+p
+0
+200
+400
+600
+800
+1000
+1200
+1400
+1600
+1800
+0.136
+0.137
+0.138
+0.139
+0.140
+c
+p
+0
+0.02
+0.04
+0.06
+0.08
+0.1
+0.136
+0.137
+0.138
+0.139
+0.140
+P
+p
+Figure 4: Boundary percolation study in the 3D random percolation model. Binder cumulant U (a),
+susceptibility χ (b), and fraction of sites occupied by largest cluster P (c) vs. fraction of positive
+sites, p. Triangles are 403, boxes 643, ×’s 1003, and open circles 1283. Error bar ranges for U are
+about 1/30 the size of plotted points, between 1/4 and 1/10 for χ, and 1/15 for P.
+7
+
+respective exponents and plotted against the scaling variable
+x = (p − pc)L1/ν
+(6)
+where L is the linear lattice size. Fig. 4abc shows the data for U, χ and P as a function
+of the concentration of positive links p for lattices of size 403, 643, 1003, and 1283. All
+datapoints are from samples of 100,000 randomly generated lattices. One sees a crossing
+in U, similar to the case of a thermal phase transition. Here the crossing point marks
+the infinite-lattice percolation threshold. Fig. 5ab shows the scaling collapse plots, where
+ν, β, γ and pc are adjusted to give the best collapse. Here the scaled χ is χL−γ/ν and
+scaled P is PLβ/ν. Although a good fit can be achieved using all four lattice sizes, a small
+systematic shift was seen in exponents toward typical percolation values when the 403 data
+were omitted, suggesting a small correction-to-scaling effect of order the random error. For
+this fit there are 65 degrees of freedom overall and the fit to the three universal functions (in
+this case power laws) has χ2/d.f= 0.77. The fit gives ν = 0.872(4), β/ν = 0.472(3), γ/ν =
+2.056(4) and pc = 0.137317(5). The latter agrees with that determined from finite-size shift
+above as well as with the threshold previously measured for NN+NNN site percolation,
+pc = 0.1372(1)[3], which we believe to be equivalent to boundary percolation. As far as
+we know exponents have not been previously measured for these cases. The quantities γ/ν
+and β/ν should be related by the hyperscaling relation
+γ/ν + 2β/ν = d
+(7)
+where d is the spatial dimension.
+Our values give, for the LHS, 3.001(7).
+For ran-
+dom site percolation a fairly recent high statistics study gives ν = 0.8764(11) and
+β/ν = 0.47705(15)[6]. Comparing with our result leads to the conclusion that all of the
+exponents for random boundary percolation likely match those of ordinary site percolation.
+For random boundary percolation, finite-size shift and largest cluster scaling give con-
+sistent measurements of ν. However that is not the case for boundary percolation in the
+3D Ising model. Figs. 6abc and 7ab analyze the largest cluster scaling for boundary perco-
+lation in the 3D Ising model in the same way as above. Of course now the abscissa is the
+Ising coupling strength κ. The study was similar to the above but with 1,000,000 sweeps
+per point, sampled every 10, and 200,000 initial equilibration sweeps on 403, 643 and 1003
+lattices. Again we have a Binder cumulant crossing and excellent scaling collapse plots.
+These give κc = 0.247925(6), ν = 0.867(5), β/ν = 0.465(5), and γ/ν = 2.068(20). So there
+are no surprises here as these exponents are consistent with the random percolation values.
+The fraction of minority sites at κc is 0.1318(4), about 4% lower than for random percola-
+tion. However, the finite-size-shift exponent, ν, obtained above from the fit to Fig. 2b was
+1.30(3) . This is clearly incompatible with the percolation value just obtained from largest
+cluster scaling in the same system. This would seem to indicate that some other dynam-
+ics has taken over the scaling of the finite-size shift, driven by another correlation length
+which is becoming infinite at a different rate. One possibility for how this could happen
+is if the percolation is linked to a thermal phase transition which has its own correlation
+8
+
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.40
+0.45
+0.50
+0.55
+0.60
+0.65
+-0.2
+-0.1
+0.0
+0.1
+0.2
+0.3
+0.4
+Scaled P
+U
+x
+0.05
+0.06
+0.07
+0.08
+-0.2
+-0.1
+0
+0.1
+0.2
+0.3
+0.4
+Scaled c
+x
+Figure 5: Scaling collapse plots for boundary percolation in the 3D random percolation model.
+Binder cumulant (left graph) and scaled largest-cluster fraction (a), and scaled susceptibility (b).
+length controlled by different dynamics. This is a very curious behavior that invites further
+investigation because, as previously mentioned, it is quite unusual for a system to have two
+different correlation lengths.
+3
+Dual order parameter
+As is well known, percolations are not necessarily coincident with phase transitions, but
+sometimes are. The situation is clearer if a symmetry-breaking order parameter exists. In
+that case an energy singularity follows from the hyperscaling relation α = 2 − dν, where
+α is the specific heat exponent, d is the number of dimensions and ν is the correlation
+length exponent associated with the order parameter near the symmetry-breaking phase
+transition. The spontaneous breaking of an exact symmetry is always associated with a
+mathematical singularity because the order parameter is exactly zero in the unbroken phase,
+and is non-zero in the broken phase[9]. A function which is zero over a range of values can
+only become non-zero at a point of non-analyticity.
+In order to build further evidence of a phase transition at the point of boundary per-
+colation, one can examine the dual theory, the three-dimensional gauge Ising model. This
+has action
+S = −β
+�
+p
+Up
+(8)
+where Up is the product of four gauge fields Uµijk around an elementary plaquette. The Uµijk
+exist on links with µ a direction index and ijk the site address. The duality relation maps
+the coupling of the Ising model κ to β of the dual gauge theory, β = −0.5 ln(tanh(κ))[10].
+The ordered phase of the spin theory maps to the disordered (confining) phase of the
+gauge theory. Generally it is not considered that there is a local symmetry-breaking order-
+parameter in gauge theories, because Elitzur’s theorem[11] does not allow a local symmetry
+9
+
+0.20
+0.25
+0.30
+0.35
+0.40
+0.45
+0.50
+0.55
+0.60
+0.65
+0.70
+0.244
+0.245
+0.246
+0.247
+0.248
+0.249
+0.25
+U
+k
+0
+100
+200
+300
+400
+500
+600
+700
+800
+900
+0.244
+0.245
+0.246
+0.247
+0.248
+0.249
+0.25
+c
+k
+0
+0.02
+0.04
+0.06
+0.08
+0.1
+0.12
+0.14
+0.244
+0.245
+0.246
+0.247
+0.248
+0.249
+0.25
+P
+k
+Figure 6: Boundary percolation study in the 3D Ising model. Binder cumulant U (a), susceptibility
+χ (b), and fraction of sites occupied by largest cluster P (c) vs. coupling κ. Error bar ranges for U
+are about 1/30 the size of plotted points, 1/20 for P, and between 1/5 and 1/20 for χ.
+to break spontaneously. However, if one transforms configurations to Coulomb gauge then
+a symmetry-breaking order parameter may be defined, for which the remnant symmetry
+breaks in the deconfined phase[12]. The Coulomb gauge transformation seeks to maximize
+the number of positive links in the one and two directions, ignoring the third direction
+links.
+This leaves a remnant layered Z2 symmetry.
+Two-dimensional global symmetry
+operations applied to single 1-2 layers do not alter the one and two direction links on
+which Coulomb gauge is defined, but flip all third direction links attached to the layer.
+For fixed one and two direction links the third direction links have mostly ferromagnetic
+interactions from plaquettes with two positive one or two direction links, especially at high
+β. If one takes the third direction links in each separate layer as order parameters, it is
+found that these magnetize exactly at the dual-reflection of the 3-d Ising critical point[13].
+10
+
+0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+-0.4
+-0.3
+-0.2
+-0.1
+0.0
+0.1
+0.2
+0.3
+P-scale
+U
+x
+0
+0.01
+0.02
+0.03
+0.04
+0.05
+0.06
+0.07
+-0.4
+-0.3
+-0.2
+-0.1
+0
+0.1
+0.2
+0.3
+c-scale
+x
+Figure 7: Scaling collapse graphs for percolation in the 3D Ising model. Binder cumulant (left
+graph) and scaled largest-cluster fraction (a), and scaled susceptibility (b).
+The deconfined phase is magnetized and the confined phase is not. The dual reflection of the
+boundary-percolation point lies in the confined phase, ie. the non-magnetized phase of the
+gauge theory. If there is a symmetry-breaking phase transition here it must be a spin-glass
+transition, which is a symmetry-breaking transition within the unmagnetized phase. A spin
+glass has a hidden pattern of order which does not result in an overall magnetization. To
+search for such a transition we used a two-real-replica approach[15]. A second set of third-
+direction pointing links is equilibrated to a fixed pattern of one and two direction links
+from the main simulation. This is similar to the initial equilibration for any Monte-Carlo
+simulation. Then the order parameter is defined as
+qk =
+�
+i,j
+R3ijkU3ijk.
+(9)
+Here R3ijk is the replica third-direction link at site ijk and U3ijk is the original one. Note
+there is a separate qk for each 2D layer, because the symmetry being broken is only global
+in two directions but still local in the third direction. As is usual one needs to take the
+absolute value of the order parameter due to tunneling on the finite lattices. We also choose
+to take the square root of the order parameter since it is the product of two spins, but this
+is not absolutely necessary. Thus the average spin-glass magnetization to be analyzed is
+M ≡<
+�
+|qk| >
+(10)
+where the average is both over gauge configurations as well as third direction fixed 2D
+layers in each gauge configuration. The order parameter M will become non-zero in a phase
+with either spin-glass order or ferromagnetic order. Spin-glass order is symmetry breaking
+because the symmetry operation applied only to the original U’s but not the replicas will
+invert the order parameter. Another way to say this is that tunneling configurations within
+11
+
+the replica or original, where half of the lattice is flipped, do not exist in the spin-glass phase
+in the thermodynamic limit. For systems without a spin-glass phase this order parameter
+will simply turn on at the normal ferromagnetic transition (for instance, this is the case
+for Landau-gauge Higgs phase transitions in the combined Ising gauge-Higgs theory[13]).
+Note also that although its original motivation was from Coulomb gauge, qk itself is gauge
+invariant, so it is no longer necessary to fix the gauge. As detailed below, we indeed find a
+phase transition in M away from the ferromagnetic transition indicating the presence of a
+spin-glass phase. Here we can use all of the finite-size scaling techniques which have been
+developed for studying symmetry-breaking phase transitions with a local order parameter.
+0.7
+0.71
+0.72
+0.73
+0.74
+0.75
+0.76
+0.77
+0
+20000
+40000
+60000
+80000
+100000
+M
+Equilibration sweeps
+0.61
+0.615
+0.62
+0.625
+0.63
+0.635
+0.64
+0
+20000
+40000
+60000
+80000
+100000
+U
+Equilibration Sweeps
+Figure 8: Equilibration of spin-glass order parameter and Binder cumulant on a 303 lattice.
+Before studying the spin-glass order parameter M in Monte Carlo simulations, one
+must first perform an equilibration study to determine how long the replica must be equili-
+brated to obtain a truly independent configuration. One simply simulates at many different
+equilibration sweep values and watches the measured quantities approach constant values
+exponentially. We then picked equilibration amounts that insure systematic errors are less
+than 25% of random errors in the quantities measured. Detailed studies were made at gauge
+coupling β = 0.705, near the suspected critical point, for both the 303 and 503 lattices. The
+equilibration value for the 403 lattice was determined from these and the volume scaling
+suggested by them. Fig. 8ab shows the equilibration of magnetization (order parameter)
+and its Binder cumulant for the 303 lattice. Other quantities were similar. The exponential
+fits give an equilibration time constant of 14,000 sweeps. By equilibrating with 105,000
+sweeps systematic errors are brought to less than 25% of random in the planned simula-
+tions. For 503 this value was a bit surprisingly high at 700,000 sweeps. We used 190,000
+sweeps for the intermediate 403 case. These high equilibration values indicate the standard
+heat bath Monte Carlo algorithm is not working particularly well here, but it still gives
+good results if one is patient. The high number of sweeps to equilibrate are due to the fact
+that 2/3 of the links, those lying in the 1 and 2 directions are being held fixed, which erects
+more barriers that a simulation where all links participate.
+12
+
+0.3
+0.5
+0.7
+0.9
+1.1
+1.3
+0.4
+0.45
+0.5
+0.55
+0.6
+0.65
+0.7
+0.66
+0.68
+0.70
+0.72
+0.74
+M
+U
+b
+0.00
+0.50
+1.00
+1.50
+2.00
+2.50
+0.66
+0.68
+0.7
+0.72
+0.74
+x2nd/L
+b
+0
+10
+20
+30
+40
+50
+60
+70
+80
+90
+100
+0.66
+0.68
+0.7
+0.72
+0.74
+c
+b
+Figure 9: Binder cumulant (left graph) and magnetization (a), ξ2nd/L (b), and susceptibility (c) for
+the spin-glass order parameter. Error bar spreads for U and M are about 1/15 the size of plotted
+points, and 1/2 to 1/5 for ξ2nd/L and χ.
+All simulations had 100 ordinary Monte Carlo sweeps between each measurement of
+the order parameter to reduce correlations. There were 1000 measurements for each 303
+and 403 lattices and 500 for 503.
+Initial equilibration was 200,000 sweeps.
+Error bars
+were determined from binned fluctuations. Fig. 9abc shows the Binder cumulant U, order
+parameter M, susceptibility χ, and second moment correlation length[16] divided by lattice
+size, ξ2nd/L, for the three lattices. The latter, as well as the Binder cumulant, should cross
+near the infinite lattice transition point (to determine this precisely one must consider
+corrections to scaling which we do not do here). One can see a well-defined crossing in both
+near βc = 0.715. The crossings are well established. For instance the 503 value exceeds
+the 303 value at β = 0.725 by 15σ for U and 10σ for ξ2nd/L, and points above this have
+similar significances. The opposite order in the low β region is never in doubt. Indeed, here
+points here are separated by even larger amounts, exceeding 30σ. Scaling collapse plots are
+13
+
+shown in Fig. 10abc. The overall fit has 75 degrees of freedom and has a χ2/d.f.= 1.48 .
+This fit gives βc = 0.7174(3), ν = 1.27(3), β/ν = 0.058(2), and γ/ν = 1.86(2). Checking
+hyperscaling on the latter give deff = γ/ν + 2β/ν = 1.97(2). Because the order parameter
+is defined on 2-d layers, the expected value is 2.
+The dual reflection of the boundary
+percolation point of the 3D Ising model itself is −0.5 ln tanh(0.247925) = 0.70741(1). This
+is close to the βc here, but certainly not an exact match, and not within statistical errors.
+However there could be a systematic error present from corrections to scaling. Looking at
+the U crossing (Fig. 9a), it is plausible that the crossing on larger lattices could shift to this
+point. Corrections to scaling can give a slightly shifting crossing with increasing lattice size.
+There is also the possibility of a residual systematic error from insufficient equilibration.
+Although we have tried to limit this to 25% of the random error it could still have an
+effect. The fact that the ν seen here and the ν from the coupling-shift of the percolation
+transition, 1.30(3) agree within 1σ strongly supports these being dual-manifestations of the
+same transition.
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+1.2
+0.5
+0.55
+0.6
+0.65
+0.7
+-1.5
+-1.0
+-0.5
+0.0
+0.5
+1.0
+Scaled M
+U
+x
+0.0
+0.5
+1.0
+1.5
+2.0
+2.5
+-1.5
+-1.0
+-0.5
+0.0
+0.5
+1.0
+x2nd/L
+x
+0
+0.01
+0.02
+0.03
+0.04
+0.05
+0.06
+0.07
+0.08
+-1.5
+-1.0
+-0.5
+0.0
+0.5
+1.0
+Scaled c
+x
+Figure 10: Scaling collapse plots for Binder cumulant (left graph) and scaled magnetization (a),
+ξ2nd/L (b), and scaled susceptibility (c), for the spin-glass order parameter.
+14
+
+4
+Energy moments
+Since the spin-glass transition in the dual theory is symmetry breaking, Landau theory
+connects this to a thermal phase transition through the hyperscaling relation
+α = 2 − dν.
+(11)
+Here α is the specific heat exponent. At the critical point the expected behavior of the spe-
+cific heat is |T − Tc|−α. For ν = 1.3, α = −1.9. This means that the specific heat does not
+have an infinite singularity, however it does have a finite singularity. Unfortunately, when
+rounded by a finite lattice size, these are difficult to spot using finite-size scaling. Never-
+theless one can still try to fit to a fractional power, and in some cases more importantly,
+a different coefficient on each side of the transition. However, the energy moments also
+have non-singular terms. This makes fitting them more difficult than quantities based on
+the order parameter which are purely singular. The non-singular part is expected to vary
+slowly through the critical region. For this reason it affects higher moments less, and there
+is a good chance these can be fit without a non-singular part other than perhaps a constant.
+This simplifies fitting to the expected critical behavior. A study of energy moments of the
+3D Ising model itself was performed. This study had approximately 7 × 109 sweeps at each
+coupling for the 303 lattice and 2 × 109 for the 403 and 503, with measurements performed
+every other sweep. With these statistics, rather precise data can be obtained on the third
+cumulant (third central moment), defined as < (E − ¯E)3 > (3L3)2. It is this combination
+that corresponds to the derivative of the specific heat. The third cumulant is expected to
+scale as |κ − κc|−α−1, which is still a non-infinite singularity. This quantity is shown in
+Fig. 11, along with a fit to the expected critical behavior, but leaving α and κc as free
+parameters. The fit also allows for a different coefficient on the two sides of the transition.
+The result is κc = 0.2477(2), and −α−1 = 0.967(12). The coefficient ratio below and above
+the critical point is 1.287(25). The predicted ν from this α is ν = (−α + 2)/3 = 1.322(4).
+The critical point agrees well with that extracted from percolation(0.24781(4), and the
+exponent ν also agrees with those from both percolation finite-size shift (1.30(3)) and the
+spin glass transition in the dual gauge theory(1.27(3)). Even though the singularity is non-
+infinite, it can still be seen from this fit. It is important to remember that these functions
+are singular in two ways - the fractional power and the jump in coefficient. So even if the
+power were to end up being exactly unity, that would not erase the singularity due to the
+fairly large coefficient jump, verified to 11.5σ, which can be seen in the change of slope.
+Higher moments were also measured, but even with these high statistics were somewhat
+of a disappointment due to fairly large statistical errors. Fig. 12 shows the fourth cumulant,
+(< (E − ¯E)4 > −3 < (E − ¯E)2 >2)(3L3)3.
+(12)
+This combination of moments tracks the third derivative of the internal energy with respect
+to κ. Also shown is a numerical derivative of the fit function to the third cumulant on a
+parameter spacing 1/4 of that used for the simulations. This was done instead of an exact
+derivative to simulate finite-lattice rounding, so not an exact prediction of the expected
+15
+
+-210
+-200
+-190
+-180
+-170
+-160
+-150
+-140
+-130
+0.243
+0.245
+0.247
+0.249
+0.251
+0.253
+Third Energy Cumulant
+k
+Figure 11: Third order energy cumulant, with fit to critical behavior. Here open circles are 303,
+open triangles 403, and × 503.
+behavior, but one which should be good away from the critical point. The main effect of
+the shift in slope in the third cumulant which translates to a shift in level here can be seen.
+In principle some finite-size effect could be seen in this quantity since it diverges with a
+very small exponent, but the expected ratio in peak heights between 303 and 403 is only
+(4/3)((α+2)/ν) = 1.02, much smaller than our statistical errors. A larger effect is predicted
+for the fifth cumulant (1.28), but the errors there are magnified even more. This figure
+is shown primarily to illustrate how much further one would have to go in statistics to
+see an infinite singularity in a high moment. Our program, which was run for about 24
+processor-years on PC’s, does not employ multi-spin coding. Perhaps a study that did or
+used specialized hardware could see these effects.
+5
+Conclusion
+In this paper evidence has been given for a new high-order phase transition within the or-
+dered phase of the 3D Ising model. This transition appears to be associated with boundary
+percolation. This is the percolation of dual-plaquettes that lie on the domain boundary
+between + and - spins, a type of percolation that has not been much studied. Percolation
+of domain boundaries occurs when minority sites occupy 13% or more of the lattice. It is,
+incidentally, not coincident with the roughening transition which occurs much deeper into
+the ordered phase, around κ = 0.408[17]. Because the Ising model has a formulation in
+terms of the domain boundary itself, the percolation of the boundary could be important,
+16
+
+3000
+4000
+5000
+6000
+7000
+8000
+9000
+0.244
+0.246
+0.248
+0.25
+0.252
+Fourth Energy Cumulant
+k
+Figure 12: Fourth order energy cumulant for 303 and 403 lattices. Line is a plausible rounded critical
+behavior based on third cumulant fit (see text).
+possibly producing a sudden change in the entropy function expressed in terms of boundary
+area.
+Random boundary percolation appears to have the same critical exponents as ordinary
+site percolation. Boundary percolation in the Ising model seems to model random boundary
+percolation as far as the scaling of cluster sizes is concerned, however it differs in the finite-
+size shift exponent, which determines how the percolation threshold depends on lattice
+size. Whereas random percolation has a shift exponent agreeing with typical values of the
+correlation-length exponent from cluster size scaling (ν ∼ 0.88), the shift exponent from
+the 3D Ising model boundary percolation is vastly different, ν ∼ 1.3. This surprising result
+means that the system has two different correlation lengths, both diverging at the infinite-
+lattice percolation threshold. This also suggests that there is more than just percolation
+going on here. If percolation is linked to a thermal phase transition, that could explain
+the odd shift exponent, since the order parameter of the phase transition may have its own
+correlation length.
+To find such an order parameter we examined the dual system, the 3D gauge Ising
+model. The dual point of the boundary percolation threshold occurs in the random (con-
+fining) phase of the gauge theory. An order parameter for the confinement-deconfinement
+transition can be obtained in Coulomb gauge, where as many one and two direction links
+as possible are made to be positive by gauge transformations. The third direction links on
+each lattice layer can be taken to be a spin-like order parameter, which shows spontaneous
+magnetization in the ordered phase and is unmagnetized in the random phase. If there is
+a phase transition corresponding to boundary percolation in the Ising model itself, it must
+occur within the random phase of the gauge theory. This suggests looking for a spin-glass
+transition here, a shift from a completely disordered phase to one with a hidden pattern
+of order, but still showing no net magnetization. To this end we utilized a two-real-replica
+17
+
+order parameter, which indeed does show a phase transition near the dual reflection of
+boundary percolation, and with the same critical exponent ∼ 1.30. This is significant be-
+cause it is a true symmetry-breaking phase transition. The symmetry being broken is the
+layered remnant (Z2)L symmetry left over after Coulomb gauge fixing, which is global in
+two dimensions but still local in the third. This is “global enough” to avoid Elitzur’s theo-
+rem and has sufficient dimensions (2) for a discrete symmetry to break spontaneously at a
+finite coupling. Spontaneous symmetry-breaking always results in a phase transition, i.e. a
+mathematical singularity in the order parameter, which also results in an energy singularity
+except in a few unusual cases [14].
+Finally we examined energy moments in search of this singularity.
+Because of the
+high value of ν the specific heat exponent is negative, implying a finite singularity, so the
+usual finite-size scaling applied to peak heights cannot be used here. We concentrated on
+the third energy cumulant, since it could be fit without the addition of an obfuscating
+non-singular part, other than a constant. An open fit to the singular form expected for
+this quantity based on the hyperscaling relationship, gives κc and ν values consistent with
+those determined by boundary percolation and the dual order parameter. There is also
+a noticeable jump in coefficient here, another expectation of this sort of singularity. Our
+study did not have enough statistics to see the small expected peak scaling in the fourth
+cumulant or somewhat larger effect in the fifth, which should have infinite singularities
+on the infinite lattice.
+Although observing these would be satisfying, still the singular
+fit to the third cumulant does match well with the prediction from the order parameter.
+This demonstrates that phase transitions as weak as these can be studied by numerical
+methods. The existence of an order parameter and associated symmetry breaking is key
+in establishing this as a true phase transition. The coincidence of boundary percolation is
+also interesting and gives another measure of ν, but cannot by itself be used to imply the
+presence of a phase transition. However, it has the advantage of being very easy to measure.
+It appears to have the same cluster-size scaling exponents as ordinary site percolation, but a
+different threshold. It may be interesting to explore boundary percolation in other systems.
+Since percolation has so many practical applications, it’s possible boundary percolation is a
+better fit than site or link percolation in some cases. Finally, we note that a previous study
+of the Z2 gauge-Higgs system showed a total of four phase transition lines further into the
+diagram[13]. The current paper shows there are two phase transitions on each axis, gauge
+and Higgs, so also a total of four. It will be interesting to follow these new phase transitions
+into the phase diagram to see how they connect with the lines previously found.
+The
+previous paper showed that the Z2 gauge-Higgs system appears to be more complicated
+than previously thought.
+The present paper shows that these additional complications
+extend to the 3D Ising model itself, and its dual, the 3D gauge Ising model.
+It seems
+possible that similar weak phase transitions may also be lurking in other well-known spin
+and gauge systems.
+18
+
+References
+[1] R.P. Feynman, Statistical mechanics - a set of lectures, Addison-Wesley, Reading MA,
+1998, ch.5.
+[2] M. Kac and J.C. Ward, A combinatorial solution of the two dimensional Ising model,
+Phys. Rev. 88, 1332-1337 (1952).
+[3] L. Kurzawski and K. Malarz, Simpe cubic random-site percolation thresholds for com-
+plex neighborhoods, Rep. Math. Phys. 70, 163-169 (2012); C. Domb and N.W. Walton,
+Crystal statistics with long-range forces I. The equivalent neighbor model, Proc. Phys.
+Soc. 89, 859-871 (1966).
+[4] H. M¨uller-Krumbhaar, Percolation in a lattice system with particle interaction, Phys.
+Lett. A 50, 27-28 (1974).
+[5] A.M. Ferrenberg and D.P. Landau, Critical behavior of the three-dimensional Ising
+model: A high-resolution Monte Carlo study, Phys. Rev. B 44, 5081-5091 (1991).
+[6] J. Wang, Z. Zohu, W. Zhang, T.M. Garoni, and Y. Deng, Bond and site percolation
+in three dimensions, Phys. Rev. E 87, 052107 (2013); Erratum, 89, 069907 (2014).
+[7] D. Stauffer and A. Aharony, Introduction to Percolation Theory, Revised 2nd edition,
+Taylor and Francis, London, 1994.
+[8] K. Binder and D.W.Heermann, Monte Carlo simulation in statistical physics - an
+introduction, 6th ed., Springer Nature, Cham Switzerland, 2019.
+[9] L.D. Landau and E.M. Lifshitz, Statistical Physics - Vol. 5 of the Course of Theoretical
+Physics, Pergamon Press, London, 1958, p452.
+[10] H.A. Kramers and G.H. Wannier, Statistics of the two-dimensional ferromagnet Part 1,
+Phys. Rev. 60, 252-262 (1941); R. Savit, Duality in field theory and statistical systems,
+Rev. Mod. Phys. 52, 453-487 (1980).
+[11] S. Elitzur, Impossibility of spontaneously breaking local symmetries, Phys. Rev. D12,
+3978-3982 (1975) .
+[12] J. Greensite, S. Olejn´ık, and D. Zwanziger, Coulomb energy, remnant symmetry, and
+phases of non-Abelian gauge theories, Phys. Rev. D 69, 074506 (2004); D. Zwanziger,
+No confinement without Coulomb confinement, Phys. Rev. Lett. 90, 102001 (2003).
+[13] M. Grady, Exploring the 3D Ising gauge-Higgs theory in exact Coulomb gauge and
+with a gauge-invariant substitute for Landau gauge, arXiv:2109.04560 (2021).
+[14] ibid Appendix A.
+[15] K. Binder and W. Kob, Glassy Materials and Disordered Solids, World Scientific, New
+Jersey, 2005, pp. 248, 261.
+19
+
+[16] F. Cooper, B. Freedman, and D. Preston, Solving φ4
+1,2 field theory with Monte Carlo,
+Nucl. Phys. B 210, 210-228 (1982); D.J. Amit and V. Mart´ın-Mayor, Field Theory,
+the Renormalization Group, and Critical Phenomena: Graphs to Computers, 3rd ed.,
+World Scientific, Singapore, 2005.
+[17] K.K. Mon, S. Wansleben, D.P. Landau and K. Binder, Anisotropic surface tension,
+step free energy, and interface roughening in the three-dimensional Ising model, Phys.
+Rev. Lett. 60, 708-711 (1988); Erratum, 61, 902 (1988); K.K Mon, D.P. Landau, and
+D. Stauffer, Interface roughening in the three-dimensional Ising model, Phys. Rev. B
+42, 545-547 (1990).
+20
+

4tFKT4oBgHgl3EQfRy39/content/2301.11773v1.pdf

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:03aa441c55a0b6aac2dd2bf488e85d43c67d4c85aee6267dbf9508b6908655ff
+size 4944672

4tFKT4oBgHgl3EQfRy39/vector_store/index.faiss

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:3d32002281639333b4b6521356454658767c704d6108bbe13b6974cc712f0328
+size 12058669

4tFKT4oBgHgl3EQfRy39/vector_store/index.pkl

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:fed0c14e37ce8c1af5b58f6dfb4303701015c555433e5ade5e00f2c1b2a3eefc
+size 347660

59E0T4oBgHgl3EQfvwFr/content/2301.02622v1.pdf

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e62e6883d9cdcde90c5ed707f23e9272b00a20b6892dba6deb00da9e5caa0adb
+size 5058457

59E0T4oBgHgl3EQfvwFr/vector_store/index.pkl

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d6c3b435e6117b20572c3c103d2b15092700491bbaceb43635e86a53544ba977
+size 277131

5tFIT4oBgHgl3EQf8CtK/content/2301.11400v1.pdf

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:482273e2f21e300ef8f681cdc350a945d6faf22c3cb51c47e8a028df885283f9
+size 4456755

5tFIT4oBgHgl3EQf8CtK/vector_store/index.pkl

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:43522b2af2f12d6829e7355bd8cb9d5c96e10c4f2ac3d257e7ee3221a19d5425
+size 1699971

69E1T4oBgHgl3EQfBgJT/content/tmp_files/2301.02852v1.pdf.txt

@@ -0,0 +1,1274 @@
+Coherent control of wave beams via unidirectional evanescent modes excitation
+Shuomin Zhong1*,∗ Xuchen Wang2*, and Sergei A. Tretyakov3
+1. School of Information Science and Engineering, Ningbo University, Ningbo 315211, China
+2. Institute of Nanotechnology, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany
+3. Department of Electronics and Nanoengineering, Aalto University, Finland
+Conventional coherent absorption occurs only when two incident beams exhibit mirror symmetry
+with respect to the absorbing surface, i.e., the two beams have the same incident angles, phases,
+and amplitudes. In this work, we propose a more general metasurface paradigm for coherent perfect
+absorption, with impinging waves from arbitrary asymmetric directions. By exploiting excitation of
+unidirectional evanescent waves, the output can be fixed at one reflection direction for any amplitude
+and phase of the control wave. We show theoretically and confirm experimentally that the relative
+amplitude of the reflected wave can be tuned continuously from zero to unity by changing the phase
+difference between the two beams, i.e. switching from coherent perfect absorption to full reflection.
+We hope that this work will open up promising possibilities for wave manipulation via evanescent
+waves engineering with applications in optical switches, one-side sensing, and radar cross section
+control.
+I.
+INTRODUCTION
+Coherent control of propagation of a wave beam by
+tuning the amplitude and phase of another beam is a very
+promising approach to realize ultra fast optical devices
+for optical computing, sensing, and other applications [1–
+11]. One of the most important effects in coherent control
+of light is coherent perfect absorption [12–22]. In these
+devices, the level of absorption of one beam illuminating
+a thin sheet is controlled by another coherent beam that
+illuminates the same sheet.
+In earlier works, coherent perfect absorption (CPA)
+was achieved only when with illumination from different
+sides of a homogeneous lossy layer and for two incident
+waves at the same angle [12, 13, 15, 22].
+The mecha-
+nism of coherent perfect absorption is destructive cancel-
+lation of all scattered beams. For homogeneous coher-
+ent perfect absorbers, there are only specular reflection
+and non-diffractive transmission, allowing coherent ab-
+sorption only with illumination of both sides and at the
+same incidence angle. From the theoretical point of view
+and for many applications, it is important to achieve co-
+herent control of output for illuminations from the same
+side of the metasurface sheet at two or more arbitrary
+incidence angles. In Refs. [17, 18, 23], coherent perfect
+absorption and scattering for two angularly asymmetric
+beams are realized by using surface plasmon-polariton
+(SPP) excitation at silver-based diffraction groove grat-
+ings. However, such plasmonic grating designs have limi-
+tations. In particular, the structures are non-planar and
+operate only for TM modes at optical frequencies, where
+SPP are supported. Moreover, there are always two out-
+put beams for different values of the phase of the control
+waves, one of which may cause undesired noise to the
+useful output signal due to parasitic scattering. This is-
+sue is critical in applications such as optical computing
+[24].
+∗ Email: [email protected], [email protected]
+In this decade, the emergence of gradient metasurfaces
+[25–28] and metagratings [29–35] has opened a new av-
+enue for manipulation of light for arbitrary incidence an-
+gles and versatile functionalities. For periodical metasur-
+faces or metagratings with the period larger than half of
+the wavelength, the incident plane wave from one direc-
+tion will be scattered into multiple directions, and the
+power carried by the incident wave can be redistributed
+among a number of diffraction modes.
+Based on this
+concept, several metasurface devices with perfect anoma-
+lous reflection working at microwaves [36, 37] and optical
+bands [38] have been developed. However, in these previ-
+ous works, the functionality of metasurfaces is designed
+only for one incident angle and the response for other illu-
+minations is actually not considered. To design metasur-
+faces with coherent control functions for multiple simul-
+taneously incident coherent beams from different direc-
+tions, the matching conditions of amplitude, phase, and
+wavevector(direction) of the scattering modes between all
+incidences are required [35, 39, 40], which is almost an
+impossible task using traditional gradient phase methods
+[25, 36] and brute-force numerical optimizations [37, 41].
+In this work, we perform inverse designs of CPA meta-
+surfaces by solving the surface impedance satisfying the
+boundary condition determined by two coherent incident
+waves from two arbitrary angles and the desired total
+scattered waves.
+The engineering of evanescent waves
+in the scattered fields without altering the desired far-
+field outputs provides significant freedom in the CPA
+metasurface design, making another functionality of co-
+herent control of reflection with a single direction possi-
+ble. It is demonstrated that excitation of unidirectional
+evanescent waves propagating along the surface in the
+direction of the incident-wave wavevector can be used to
+achieve single-direction output in coherently controlled
+optical devices. Furthermore, a mathematical optimiza-
+tion method based on scattered harmonics analysis [42]
+is utilized to find the surface-impedance profile that si-
+multaneously ensures the CPA and coherent maximum
+reflection (CMR) in a single direction. Thereafter, the
+arXiv:2301.02852v1  [physics.app-ph]  8 Jan 2023
+
+2
+substrate parameters are invoked as additional degrees of
+freedom in the optimization model, realizing reflection ef-
+ficiency of 100%. As an example, we experimentally vali-
+date the CPA gradient metasurface design in microwaves
+for TE-polarized waves by engineering the Indium Tin
+Oxide (ITO) film mounted on a grounded dielectric sub-
+strate. It is showed that the normalized output power
+can be continuously controlled between 0 and 1 by tun-
+ing the phase of the control wave.
+II.
+DESIGN CONCEPT
+Dx 
+x 
+z 
+Zs(x) 
+θ1 
+θ2 
+I1 
+I2 
+FIG. 1. General scattering scenario for a periodically modu-
+lated impenetrable impedance surface. Two coherent beams
+I1 and I2 are simultaneously incident from two angles.
+Let us consider an impenetrable reciprocal metasur-
+face whose surface is periodically modulated along the
+x-direction, with the period Dx. The surface is in the
+xy-plane of a Cartesian coordinate system (see Fig. 1).
+The metasurface is simultaneously illuminated by two
+TE(s)-polarized plane waves I1 and I2 at the incidence
+angles θ1 and θ2 (θ1 > θ2). The electric field amplitudes
+of the two beams I1 and I2 is E1 = E0 and E2 = αE0,
+respectively (α is the amplitude ratio). The phase differ-
+ence between them is ∆φ=0, defined at the origin point
+(x = 0, z = 0). The electromagnetic properties of the
+metasurface can be characterized by the locally-defined
+surface impedance that stands for the ratio of the tangen-
+tial electric and magnetic field amplitudes at the surface
+plane Zs(x) = Et(x)/Ht(x).
+The field reflected by a periodically modulated meta-
+surface can be interpreted as a sum of Floquet harmonics.
+The tangential wavenumber of the n-th harmonic is re-
+lated to the period and the incident wavenumber k0 as
+krxn = k0 sin θi + 2πni/Dx, where i = 1, 2. The corre-
+sponding normal component of the reflected wavenumber
+equals krzn =
+�
+k2
+0 − k2rxn. If |krxn| is greater than the
+incident wave number, the wave is evanescent and it does
+not contribute to the far field. For the harmonic wave sat-
+isfying |krxn| < k0, krzn is real, and this wave is propagat-
+ing. The evanescent harmonics will be dissipated by the
+lossy surface and the propagating harmonics will propa-
+gate into the far-zone at the angles θrn = arcsin(krxn/k0).
+In order to achieve coherent perfect absorption, it is nec-
+essary (but not sufficient) to ensure that all the diffracted
+propagating modes of two beams have the same set of
+angles θrn, that allows mutual cancellation, defining the
+period Dx = λ0/(sin θ1 −sin θ2) [43], where λ0 stands for
+the wavelength.
+Our aim is to achieve coherent perfect absorption for
+two coherent in-phase waves simultaneously incident on
+the metasurface at two different angles θ1 and θ2. First,
+let us assume that no evanescent waves are excited for
+these two illuminations. In the CPA case, there should
+be no reflected field at the surface. Thus, the tangential
+components of the total electric field at the plane z = 0
+can be written as Et(x) = E0(e−jk0 sin θ1x+αe−jk0 sin θ2x),
+where the time-harmonic dependency in the form ejωt
+is assumed and suppressed.
+The corresponding total
+magnetic field reads Ht(x) = E0(cos θ1e−jk0 sin θ1x +
+α cos θ2e−jk0 sin θ2x)/Z0, with Z0 =
+�
+µ0/ϵ0 being the
+free-space wave impedance. The ratio of these electric
+and magnetic fields gives the required surface impedance
+ℜ(Zs) = Z0
+cos θ1 + α2 cos θ2 + α cos Φ(cos θ1 + cos θ2)
+cos2 θ1 + α2 cos2 θ2 + 2α cos θ1 cos θ2 cos Φ ,
+ℑ(Zs) = Z0
+α(cos θ1 − cos θ2) sin Φ
+cos2 θ1 + α2 cos2 θ2 + 2α cos θ1 cos θ2 cos Φ,
+(1)
+where Φ = k0(sin θ1 − sin θ2)x is the linearly varying
+phase.
+The real and imaginary parts of the surface
+impedance are even and odd functions of x, respectively.
+As is seen from Eqs. (1), the periodicity of the surface
+impedance is D = λ0/(sin θ1 − sin θ2), in accord with the
+above analysis. For passive metasurfaces, the real part
+of the surface impedance must be non-negative.
+Con-
+sequently, the amplitude ratio should satisfy α ≥ 1 or
+α ≤ cos θ1/ cos θ2 to ensure passive solution for CPA by
+the surface.
+As an example, we consider two incident waves with
+incidence angles of (θ1, θ2) = (45◦, 0◦) and the same am-
+plitude, assuming α = 1 for simplicity. (Other scenarios
+with (θ1, θ2) = (60◦, −30◦), (75◦, 15◦) are illustrated in
+the Supplemental Materials[43], corresponding to differ-
+ent surface impedance profiles.) As is shown in Fig. 2(a),
+everywhere on the surface its resistance is non-negative,
+demonstrating that passive gradient periodic surfaces can
+realize CPA for two asymmetric incident beams.
+To analyze the mechanism of CPA by the periodic
+impedance surface further, we can determine the ampli-
+tudes of all the Floquet scattered harmonics for general
+plane-wave illumination, using the method reported in
+[42]. The total reflected field can be represented as an
+infinite sum of Floquet harmonic modes:
+Er =
+∞
+�
+n=−∞
+Ane−jkrznze−jkrxnx,
+(2)
+where An is the complex amplitude of the n-th Floquet
+harmonic. Because the surface modulation is periodical,
+the surface admittance Ys(x) = 1/Zs(x) can be expanded
+
+3
+0
+0.2
+0.4
+0.6
+0.8
+1
+-200
+0
+200
+400
+(a)
+-8
+-6
+-4
+-2
+0
+2
+4
+6
+8
+0
+0.1
+0.2
+0.3
+0.4
+0.5
+(b)
+0
+0.2
+0.4
+0.6
+0.8
+1
+-200
+0
+200
+400
+(c)
+-6
+-4
+-2
+0
+2
+4
+6
+8
+0
+0.1
+0.2
+0.3
+0.4
+0.5
+(d)
+FIG. 2. (a) Analytical surface impedance over one period to realize CPA for two incidence beams with (θ1, θ2) = (45◦, 0◦).
+(b) Magnitudes of the complex amplitudes of different Floquet scattered harmonics (normalized by the amlpitude of the
+incident electric field E0) when the gradient surface is illuminated by single-beam incidences at 45◦ and 0◦, and for two-
+beam incidences in phase and out of phase, respectively. (c) Optimized surface impedance profile over one period to realize
+CPA for in-phase incidences and single-direction reflection for out-of-phase incidences.
+The optimized Fourier coefficients
+of Ys(x) read g0 = 2.654 × 10−3 + j1.724 × 10−11, g1 = −7.770 × 10−4 − j1.045 × 10−10, g2 = −(6.565 + j4.581) × 10−5,
+g3 = −9.143×10−8 +j5.720×10−6, g4 = (−1.644+j1.992)×10−5. (d) Amplitudes of scattered harmonics when the optimized
+gradient surface in (c) is illuminated by single-beam incidences at 45◦ and 0◦, and for two-beam incidences in phase and out
+of phase, respectively.
+into Fourier series:
+Ys(x) =
++∞
+�
+n=−∞
+gne−j2nπx/D.
+(3)
+A Toeplitz matrix Ys which we call the admittance ma-
+trix is determined only by the Fourier coefficients of the
+modulation function and filled with Ys(r, c) = gr−c at
+the r-th row and c-th column. The reflection matrix is
+found as [44]
+Γ = (Y0 + Ys)−1 (Y0 − Ys),
+(4)
+where Y0 = Z−1
+0
+is a diagonal matrix with its main
+entry representing the admittance of each space har-
+monic, which is Y0(n, n) =krzn/ω0µ0. The amplitudes
+An of reflected harmonics for a given m-th order Flo-
+quet harmonic of the incident wave can be calculated
+as An = Γ(n, m). Note that Γ is a (2N + 1) × (2N + 1)
+square matrix and the columns and rows of Γ are indexed
+from −N to +N. When the surface is illuminated by two
+waves simultaneously, the amplitudes of all the Floquet
+harmonics are linear superpositions of all harmonics.
+As is seen from Fig. 2(b), when the two incident waves
+are in phase, all the harmonics have zero amplitude,
+meaning that CPA with no reflected fields occurs. How-
+ever, when the two incident waves are out of phase, the
+reflected harmonics come out, including both propagat-
+ing modes and evanescent ones, proving that the perfect
+absorption effect is phase-coherent, different from perfect
+absorption for two angles [45]. To understand the mech-
+anism of CPA in the metasurface better, the harmonics
+
+4
+of the reflected field when single beams illuminate the
+surface separately are calculated. As shown in Fig. 2(b),
+the complex amplitudes of every scattered harmonic are
+equal and 180◦ out of phase (the phases are not shown
+here) for 45◦ and 0◦ incidences, resulting in destructive
+cancellation when the two beams illuminate simultane-
+ously in phase. Here, the propagating harmonic of the
+order n = 0 is defined at the specular direction of θ1 for
+both incidences. By properly designing the metasurface
+with the periodicity of D = λ0/(sin θ1 − sin θ2), three
+propagating modes corresponding to n = 0, −1, −2 are
+created, and all the diffracted modes for both incidences
+have the same wave vectors, ensuing coherent interfer-
+ence for all corresponding harmonics. In the out-of-phase
+incidence case, the amplitudes of all the scattered har-
+monics double as compared to the single-beam case, as
+shown in Fig. 2(b).
+The analytical method to solve the surface impedance
+boundaries used above is based on the objective to real-
+ize CPA with the amplitudes of both scattered propagat-
+ing and evanescent harmonics being zero when two co-
+herent beams illuminate the metasurface simultaneously.
+Indeed, the amplitudes of evanescent surface modes can
+be nonzero without breaking the CPA condition, because
+they do not radiate into the far zone and their power
+will be dissipated at the lossy surface.
+Thus, the so-
+lution of the surface impedance to achieve CPA is not
+unique if a certain set of evanescent waves with unknown
+complex amplitudes is excited. In addition to CPA, we
+invoke another functionality of coherent control of reflec-
+tion with single direction, i.e. eliminating the unwanted
+outgoing beams at n = −1, −2 orders and keeping the
+n = 0 order with the maximal amplitude, when the two
+coherent incident beams are out-of-phase. In this case,
+finding the complex amplitudes of infinite numbers of
+evanescent modes for each incidence scenario is difficult
+or even impossible. Thus, instead of using the analyti-
+cal method of calculating the surface impedance profile
+according to the total fields on the boundary, we ap-
+ply a mathematical optimization algorithm described in
+Ref. [42] and based on the scattering matrix calculation
+to find a surface impedance profile that simultaneously
+ensures the coherent control capability for absorption and
+reflection of the surface. First, the metasurface is mod-
+elled as in Eq. (3). To suppress propagating modes at
+the negative orders (n = −1, −2) and ensure that only
+the reflection channel at 45◦ is open, the Fourier series of
+the surface admittance Ys(x) are set to be unilateral as
+Ys(x) = �4
+n=0 gne−j2nπx/D with non-negative-order se-
+ries coefficients being nonzero (only five coefficients from
+g0 to g4 are used for improving optimization efficiency).
+This setting is reasonable because the unilateral surface
+admittance, making the admittance matrix Ys a lower
+triangular matrix, can lead to the reflection matrix Γ
+also being a lower triangular matrix, as is seen from
+Eq. (4). Consequently, the scattered modes contain only
+components of non-negative orders (n ≥ 0). This effect
+highlights the role of unidirectional evanescent fields as
+a mechanism of suppressing propagating modes at the
+negative orders (n = −1, −2). Moreover, to ensure that
+the grid is a passive metasurface, we need to impose con-
+straints ℜ(Ys) ≥ 0, i.e., ℜ(g0) ≥ |g1| + |g2| + |g3| + |g4|.
+Secondly, the optimization goal is formulated as 6 ob-
+jectives, including (|A0|, |A−1|, |A−2|) = (0, 0, 0) for the
+in-phase scenario, and (|A0|, |A−1|, |A−2|) = (A0max, 0, 0)
+for the out-of-phase scenario, where A0max is the maxi-
+mum magnitude of reflection in the out-of-phase case.
+In each trial of the optimization, an array of gn is as-
+sumed, and the value of all the objectives are calcu-
+lated using Eq.(4). The sum of errors calculated for all
+the objectives is defined as a cost function C. By em-
+ploying MultiStart and fmincon optimization algorithms,
+the maximum magnitude of the out-of-phase reflection
+A0max = 0.34 is searched out, and the minimum value
+of C close to zero is achieved, meaning that the solu-
+tions of the impedance profile to realize the desired EM
+responses including CPA and single-direction-reflection
+are obtained.
+Figure 2(c) shows a typical optimized solution of the
+surface impedance, which exhibits positive resistance ev-
+erywhere along the metasurface. The calculated ampli-
+tudes of scattered harmonics for single-beam incidences
+at 45◦ and 0◦, and for two-beam incidences in phase and
+out of phase, for the impedance profile in Fig. 2(c), are
+given in Fig. 2(d), revealing the unilateral characteristic
+of scattering. We can see that the propagating compo-
+nents at n = −1, −2 orders are suppressed successfully
+by exciting the unidirectional evanescent wave. The only
+remaining propagating reflected channel is n = 0 order
+at the outgoing angle of 45◦. When two incoming beams
+are in phase, the reflected propagating harmonic (n = 0)
+of each beam cancel each other because they have the
+same amplitude and π-reflection-phase difference. Dis-
+tinct from the zero-amplitude of all the harmonics for the
+in-phase CPA scenario in Fig. 2(b), the CPA in Fig. 2(d)
+occurs with non-zero-amplitude evanescent modes in the
+n ≥ 1 orders. The amplitude of reflected electric field
+at 45◦ (n = 0) is doubled into A0max = 0.34 when two
+incoming beams are out of phase (∆φ = π).
+We can
+conclude that the reflected power at 45◦ can be contin-
+uously controlled by phase tuning of the control beam.
+When the two beams are out of phase, the reflected power
+normalized by the incident beam power at 45◦ has the
+maximum reflection efficiency of 11.56 %.
+III.
+OPTIMIZATION AND PRACTICAL
+DESIGN
+Low efficiency of the above design based on the im-
+penetrable impedance model calls for optimization with
+the help of additional degrees of freedom. One possibility
+can be the use of one or more parameters of the actual
+implementation of the metasurface.
+In general, the impedance surface in the impenetra-
+ble model used above can be realized as a periodic metal
+
+5
+x 
+z 
+q1 
+D 
+h 
+I1
+I2
+n = 0
+n = -1
+n = -2
+FIG. 3.
+Schematics of reflection amplitude modulation for
+two coherent waves with the phase difference ∆φ incident on a
+periodic sheet over a grounded dielectric slab. The amplitude
+of the output beam is modulated continuously by varying ∆φ,
+and switched between 0 (coherent perfect absorption) and 1
+(coherent maximum reflection) when ∆φ is switched between
+even and odd multiples of π.
+pattern on a thin grounded dielectric slab, as shown in
+Fig. 3. The structure can be considered as a grid admit-
+tance of the top pattern with a shunt admittance of the
+grounded substrate. The characteristic admittance ma-
+trix Yd of the grounded substrate contains only diagonal
+terms Yd(n, n), where Yd(n, n) is the admittance of the
+n-th harmonic, and it is expressed as
+Yd(n, n) = kd
+rzn/[jµ0ω0 tan(kd
+rznh)],
+(5)
+where kd
+rzn =
+�
+ω2
+0ϵ0ϵdµ0 − k2rxn is the normal compo-
+nent of the wavevector in the substrate (see Eq.S23 of
+the Supplemental Material of [42]), ϵd and h are the
+permittivity and thickness of the substrate, respectively.
+The reflection matrix is calculated as Γ = (Y0 + Yg +
+Yd)−1(Y0−Yg−Yd). When the thickness h is ultra-thin
+compared with the wavelength, for low-order harmonics
+we have tan(kd
+rznh) ≈ kd
+rznh. As is seen from Eq. (5),
+the admittance for low-order harmonics equals approxi-
+mately to 1/(jµ0ω0h), unrelated to the harmonic num-
+ber. Thus, we can approximately design the top surface
+with the grid admittance Yg(x) = 1/Zs(x) − Yd(0, 0) us-
+ing the optimized surface impedance Zs(x) in Fig. 2(c),
+similar to Ref. [41]. Due to the lack of freedom in the sub-
+strate design, the evanescent fields engineering is quite
+limited in the impenetrable model, resulting in a low
+reflection efficiency (11.56 %) in the out-of-phase sce-
+nario. In order to implement CPA with a high reflec-
+tion efficiency, we need to use the substrate parameters
+as additional degrees of freedom in the design. Since the
+admittance of the grounded substrate with a moderate
+thickness strongly depends on the harmonic number, the
+need of complicated matrix operations makes it impos-
+sible to analytically solve the grid impedance and sub-
+strate parameters. Thus, the optimization algorithm is
+extended by introducing the admittance matrix Yd of the
+grounded substrate, as described in Ref. [42], to search
+for an optimum solution for the grid impedance profile
+and substrate thickness.
+According to the results of the impenetrable model,
+the period of the impedance sheet modulation is set
+to D = λ0/ sin 45◦, with three propagating channels at
+−45◦, 0◦, and 45◦. The Fourier series of the grid admit-
+tance is set to be unilateral as Yg(x) = g0 + g1e−j2πx/D,
+ensuring that only the reflection channel at 45◦ is open.
+In the optimization process, two Fourier terms g0 and
+g1 with four unknowns (the real and imaginary parts)
+are considered here to reduce complexity. The substrate
+thickness h is another unknown, and an available sub-
+strate with the permittivity ϵd = 5.8(1 − j0.002) is used.
+The optimization goal is formulated as 6 objectives, the
+same as the objectives in the impenetrable model above.
+The constraints ℜ(Yg) ≥ 0, i.e., ℜ(g0) ≥ |g1| are imposed
+to ensure the grid to be a passive metasurface. Addi-
+tionally, to make the reactance easier to implement by
+patterning a thin conductive surface, another constraint
+ℑ(g0) ≥ |g1| is set to ensure that the surface reactance is
+always capacitive at all points of the metasurface.
+The maximum magnitude of reflection A0max in the
+out-of-phase scenario is searched out to be about 1 in
+the optimization, meaning that a reflection beam at
+45◦ with amplitude equal to the incident beam I1 is
+obtained [46].
+It reveals that the invocation of sub-
+strate design provides an important additional degree
+of freedom in engineering auxiliary evanescent modes to
+find a surface impedance that can realize the desired
+optimum scattering properties for all incidence scenar-
+ios.
+The optimized Fourier coefficients of the grid ad-
+mittance Yg(x) read g0 = (2.599 + 7.054j) × 10−3 and
+g1 = (−0.807 + 2.463j) × 10−3. The optimal substrate
+thickness is h = 0.2525λ0. The required grid impedance
+which is passive and capacitive along the metasurface is
+shown in Fig. 4(a).
+Next, we analyse the scattered harmonics for the de-
+signed impedance sheet on the metal-backed dielectric
+substrate [see Fig. 4(b)]. The reflection coefficient of the
+metasurface has the same magnitude of 0.5 at n = 0
+order for 45◦ and 0◦ single-beam incidences, resulting
+from destructive interference when these two beams are
+in phase. For the out-of-phase scenario, the normalized
+magnitude of the reflected field at n = 0 order (45◦) is
+about unity, which means that the reflected power effi-
+ciency reaches 100% (normalized by the incoming power
+of the 45◦ beam). Parasitic reflections into other direc-
+tions (n = −1, −2) are seen to be negligible, due to the
+unilateral property of the admittance of the surface. The
+evanescent harmonics are also unidirectional, but quite
+weak with the magnitude of 0.008 at n = 1 order, and
+they are absorbed by the lossy structure, ensuring a CPA
+state. Figure 4(c) illustrates the phase-controlled modu-
+lation of reflections at three propagating orders. The re-
+flection coefficient at 45◦ can be continuously controlled
+from 0 to 1 by phase tuning, with the other two par-
+asitic reflections maintained very close to zero.
+This
+phase-sensitive modulation between CPA and coherent
+
+6
+0
+0.2
+0.4
+0.6
+0.8
+1
+-200
+-100
+0
+100
+(a)
+-8
+-6
+-4
+-2
+0
+2
+4
+6
+8
+0
+0.5
+1
+(b)
+0
+1
+2
+ ( )
+0
+0.2
+0.4
+0.6
+0.8
+1
+Amplitude (|An|/E0)
+n=0
+n=-1
+n=-2
+(c)
+𝐸𝑠𝑐/𝐸0 
+1 
+0 
+-1 
+2 
+3 
+-2 
+-3 
+Df = 0 
+Df = p 
+(d)
+FIG. 4.
+(a) The optimized and discretized grid impedance distribution over one period. (b) Amplitudes of the scattered
+harmonics when the optimized gradient metasurface is illuminated by a single beam at 45◦ and 0◦, and for two-beam in-phase
+and out-of-phase illuminations, respectively. (c) The normalized amplitudes of three propagating harmonics (n = 0, −1, −2)
+with a varying phase difference ∆φ between incidences at 45◦ and 0◦. (d) The scattered electric fields and power density flow
+distributions for the metasurface modeled by the discretized grid impedance (step-wise approximation, 6 subcells per period)
+on top of a grounded dielectric substrate. Two plane-wave incidences are in phase (left) and out of phase (right).
+maximum reflection (CMR) without parasitic reflections
+is important in light switching applications where a low-
+return-loss characteristic is required. See the Supplemen-
+tal Animation [43] for the switch of reflected beam by an
+incident phase-controlled wave.
+In implementations, the influence of discretization on
+the metasurface performance is an important factor (see
+detailed analysis of scattered harmonics versus the num-
+ber of subcells in Ref. [43]).
+We use six subcells over
+a period and each discretized impedance value is set at
+the central point of each subcell, as shown in Fig. 4(a).
+The scattered fields from the ideal impedance sheet on
+the metal-backed dielectric slab for both in-phase and
+out-of-phase incidences are presented in Fig. 4(d), using
+full-wave simulations in Comsol. The reflected field dis-
+tribution confirms that the metasurface with six subcells
+per period possesses the desired response: nearly per-
+fect absorption with reflection amplitude of only 0.023
+for two in-phase illuminations and nearly total reflection
+at 45◦ for two out-of-phase illuminations, relative to the
+intensity of the 45◦ incidence.
+It is seen that the top
+lossy sheet and reflective ground separated by the slab
+act as a leaky-wave cavity with enhanced fields. For the
+in-phase scenario, the direct reflections of the top surface
+and leaky wave components of the cavity destructively
+cancel out, and all the power is absorbed by the lossy
+surface, causing CPA. By changing the initial phase dif-
+ference between the two coherent incidences into π, con-
+structive interference occurs among these components,
+which results in nearly total reflection. Note that in the
+out-of-phase case a half of the total incoming power (two
+incident beams) is still absorbed by the lossy surface.
+IV.
+PHYSICAL IMPLEMENTATION AND
+EXPERIMENTAL VALIDATION
+The theory above is general and applies to any fre-
+quency, and we choose the microwave band for a proof
+of concept demonstration. The required impedance pro-
+file at 15.22 GHz is realized using an ITO film with the
+surface resistance of 5.5 Ω/sq supported by a grounded
+
+7
+f (GHz)
+12
+13
+14
+15
+16
+17
+18
+E/ciency
+0
+0.2
+0.4
+0.6
+0.8
+1
+90
+9-1
+9-2
+9'0
+9'-1
+9'-2
+Simulated
+(a)
+Transmitting  
+antenna 
+Receiving  
+antenna 
+Metasurface 
+Scanning track 
+(b)
+3r (deg)
+-80 -60 -40 -20
+0
+20 40 60 80
+S21;m (dB)
+-120
+-110
+-100
+-90
+-80
+-70
+-60
+3i = 0o
+3i = 45o
+(c)
+f (GHz)
+12
+13
+14
+15
+16
+17
+18
+E/ciency
+0
+0.2
+0.4
+0.6
+0.8
+1
+90
+9-1
+9'0
+Measured
+(d)
+FIG. 5.
+(a) Simulated and (d) measured reflection efficiency spectrum for different diffracted modes of each single beam at
+0◦ (solid lines) and 45◦ (dashed lines). (b) Schematic of the experimental setup (top) and photograph of the fabricated sample
+(bottom). (c) Signals at 15.22 GHz measured by the receiving antenna at different orientation angles with the transmitting
+antenna at 0◦ and 45◦.
+dielectric slab with the thickness h = 4.95 mm, as
+shown in Fig. 3.
+The detailed parameters and struc-
+tures of each unit cell are presented in the Supplementary
+Material[43]. Due to the resolution limitation of picosec-
+ond laser micro-processing, the complex grid impedance
+is implemented as six subcells, and each subcell is divided
+into four equal sub-subcells in order to make the local
+design of the gradient impedance more robust. By struc-
+turing the homogeneous resistive ITO film into I-shaped
+cells, the required grid resistance and reactance on a sur-
+face in Fig. 4(a) can be created. For y-polarization inci-
+dent waves, such I-shaped resonators can be modeled as
+RLC series circuits. The required resistance is realized by
+tailoring the width and length of the ITO strips. Smaller
+width and longer length result in higher grid resistance.
+The required reactance can be tailored by adjusting ca-
+pacitance of the gap, which can be increased by narrow-
+ing the gap or increasing the length or width of the bar,
+with a small influence on the resistive part. The 5th and
+6th subcells degenerate into strips, to implement resistive
+parts as close to the theoretical value as possible. How-
+ever, there are still deviations of 3.6 Ω and 1.1 Ω from
+the theoretical resistances of the 5th and 6th subcells,
+respectively. The deviation can be eliminated if an ITO
+film with a lower surface resistance is utilized. To sim-
+plify the fabrication process, we neglect this deviation.
+The impact is analyzed theoretically, showing that the
+reflection amplitude in the in-phase scenario increases
+from 0.023 to 0.065, which is tolerable in experiments.
+Since the two beams with 0◦ and 45◦ incidence angles
+illuminate the surface simultaneously, all the elements
+should have angle-independent surface impedances. The
+
+OLMS
+EILMS
+SWAi
+CILAS
+S-iD
+SWAiN
+SWiM
+SWi8
+I-shaped resonators have angle-insensitive impedance un-
+der TE incidences, satisfying this requirement [47]. In the
+strips of the 5th and 6th subcells, narrow slits are cut out
+to reduce the angular sensitivity of the impedance. All
+the subcells have been optimized with the geometrical
+dimensions specified in Ref. [43].
+Figure 5(a) shows the simulated frequency response of
+the metasurface for the normal and 45◦ incidences. For
+the normal illumination, strong reflections occur at n =
+−1 and n = 0 harmonics (denoted as ξ−1 and ξ0), and the
+amplitude of the n = −2 scattered propagating mode is
+nearly zero in the whole frequency band. The reflection
+at the n = −1 mode (specular reflection at 0◦) also has a
+near-zero dip at the design frequency of 15.22 GHz, and
+the reflection efficiency at the n = 0 mode(anomalous re-
+flection at 0◦) is about 13.9% (the relative amplitude is
+0.44). Note that for anomalous reflection, the efficiency
+is calculated as ξ = (Er/Ei)2cos θr/cos θi [37]. For the
+45◦ illumination, the reflections at both n = −1 and
+n = −2 modes (ξ′
+−1 and ξ′
+−2) are close to zero, and
+the efficiency at the n = 0 mode (ξ′
+0) is about 21% at
+15.22 GHz (the relative amplitude is 0.46). Therefore, at
+the operating frequency 15.22 GHz, the reflected modes
+for both incidences at the outgoing angle of 45◦ are al-
+most equal-amplitude, satisfying the condition of CPA.
+The scattered electric field distributions of the designed
+metasurface illuminated by two beams in the in-phase
+and out-of-phase scenarios obtained from full-wave sim-
+ulations are presented in Ref. [43]. It can be seen that
+when the two illuminations are in phase, the total scat-
+tered fields are quite small (0.02), indicating nearly per-
+fect coherent absorption. However, when the two illumi-
+nations are switched into the out-of-phase state, the rel-
+ative amplitude of the scattered fields is about 0.91, and
+the coherent maximum reflection is mainly along the 45◦
+direction.
+We have fabricated a sample (see Methods) and car-
+ried out several experiments to validate the theoretical
+results (see Fig. 5(b)). First, the transmitting antenna
+is fixed at 0◦, whereas the receiving antenna is moved
+along the scanning track with a step of 2.5◦. The signal
+reflected from the metasurface is measured by the receiv-
+ing antenna at different angles θr. Then, the transmitting
+antenna is fixed at 45◦ and the receiving antenna is scan-
+ning its position to measure the reflected signal in the
+other half space. As shown in Fig. 5(c), the main peaks
+of reflections for both two incidences occur at θr = 45◦,
+which is an expected result according to the theory and
+simulations. There is another reflection peak at θr = 0◦
+for the normal incidence case, which is about −10 dB
+lower than the main peak, corresponding to a low spec-
+ular reflection at 15.22 GHz.
+To estimate the amplitude efficiency of the metasurface
+at all three reflection channels, we replaced the metasur-
+face by a copper plate of the identical size and measured
+the specular reflection signal amplitudes from the refer-
+ence uniform metal mirror for θi = 2.5◦ (approximately
+normal incidence), 22.5◦, and 45◦ incidence angles. The
+specular reflection efficiency of the metasurface for 0◦ and
+45◦ illuminations are calculated by normalizing the signal
+amplitude by the amplitude of the signal reflected from
+the reference plate, illuminated at 2.5◦ and 45◦ angles, re-
+spectively. As shown in Fig. 5(d), at the design frequency
+of 15.22 GHz, the specular reflection efficiencies at 0◦ and
+45◦ (ξ−1 and ξ′
+0) equal 0.8% and 18.6% (the relative am-
+plitude is 0.431), respectively. For the anomalous reflec-
+tion at the n = 0 mode for the normal incidence, the re-
+flection angle is θr = arcsin(15.22/(
+√
+2f)), which equals
+45◦ at 15.22 GHz and varies from 63.7◦ to 36.7◦ as the
+frequency changes from 12 GHz to 18 GHz. Therefore,
+we choose the signal data of a different receiving angle θr
+calculated according to different frequency band and nor-
+malize its signal amplitude by the signal amplitude from
+the reference mirror for different θr/2 incidence angles.
+Additionally, we divide the obtained value by an esti-
+mated correction factor [37]
+�
+cos(θr)/ cos(θr/2), which
+gives the ratio between the theoretically calculated sig-
+nal amplitudes from an ideal metasurface (of the same
+size and made of lossless materials) and a perfectly con-
+ducting plate.
+At the design frequency of 15.22 GHz,
+the correction factor is equal to 0.91, thus the reflection
+efficiency is calculated as 12%(the relative amplitude is
+0.412), as shown in Fig. 5(d). The measured efficiency is
+in good agreement with the results obtained using numer-
+ical simulations (see Fig. 5(a)), except for some ripples in
+the ξ0 curve caused by the discrete angular scanning step
+in the measurement. The relative amplitudes of reflec-
+tions for both incidences at the n = 0 mode are almost
+equal in the measurements, verifying the capability for
+CPA.
+To experimentally verify the phase-controlled reflec-
+tion by the metasurface, in the last measurement shown
+in Fig. 6(a), two transmitting antennas fed via a power
+divider illuminate the metasurface normally and at 45◦.
+A receiving antenna is placed at the 45◦ angle to mea-
+sure the total power reflected by the metasurface under
+two simultaneous illuminations. To avoid severe insertion
+loss caused by the use of a phase shifter in one branch,
+which may increase the amplitude inequality between two
+beams, we mimic the phase-difference-tuning process by
+moving the metasurface along the x direction. As seen in
+Fig. 6(b), the phase difference between the two beams is
+linearly varying when we change the horizontal position
+of the metasurface. Therefore, this shift is equivalent to
+a phase change between the two beams. To ensure the
+effectively-illuminated area of the metasurface to remain
+stable during the moving process, we put two pieces of ab-
+sorbing foam on top of both sides of the sample. The to-
+tal received power, normalized by the maximum power of
+reflected wave is changing with varying the distance ∆x.
+As is seen in Fig. 6(c), the modulation depths reach 0.15
+and 0.04 at 15.22 GHz and 15.47 GHz, respectively. This
+result indicates that coherent enhancement and cancella-
+tion near the design frequency can be achieved by tuning
+the phase difference of the two incident beams. The pe-
+riod of the modulation is about 29 mm, almost equal to
+
+9
+Receiving  
+antenna 
+Transmitting  
+antenna 1 
+Transmitting  
+antenna 2 
+Moving direction 
+Absorbing 
+ foam 
+Absorbing  
+foam 
+                                    
+(a)
+∆∅ = 2𝜋∆𝑥/𝐷 
+𝜃 
+∆∅ 
+O’ 
+O 
+(b)
+"x (mm)
+0
+10
+20
+30
+40
+Normalized Recieved Power
+0
+0.2
+0.4
+0.6
+0.8
+1
+13GHz
+15.22GHz
+15.47GHz
+17GHz 
+(c)
+FIG. 6.
+(a) Experimental setup. Two transmitting antennas fed via a power divider illuminate the metasurface normally and
+at 45◦. A receiving antenna is placed at 45◦ to measure the total reflected power. Due to the periodicity of the metasurface,
+continuously-changing phase difference between the two beams can be emulated by moving the metasurface horizontally along
+the impedance variation direction. Two pieces of absorbing foam are put on both sides, ensuring that the effective exposure
+area of the metasurface remains fixed when the surface is shifted. (b) The reference point O is the intersection point of the 0◦
+and 45◦ beams on the metasurface when the phase difference is 0. The phase difference at a distance ∆x from the reference
+point O is ∆φ = 2π∆x/D, which is linearly varying as a function of the horizontal distance ∆x. (c) The normalized received
+power for different metasurface positions at 13, 15.22, 15.47, and 17 GHz.
+the period of the metasurface, which validates the theo-
+retical analysis. However, at the frequency far from the
+designed one, for instance at 13 GHz and 17 GHz, the
+coherent phenomenon becomes much weaker, as is seen
+in Fig. 6(c), due to a mismatch of the main reflection
+angles and the reflection amplitudes of the normally and
+obliquely incident waves.
+V.
+DISCUSSION
+We have demonstrated coherent perfect absorption of
+two beams incident at arbitrary angles. It has been found
+that this effect is possible for relative beam amplitudes
+within a certain range using a gradient passive planar
+structures. When these two incidences change into out-
+of-phase state, reflections at all three propagating chan-
+nels come out. To realize coherent control of reflection
+with single direction, the other parasitic reflections can
+be suppressed by introducing unidirectional evanescent
+modes excitation. To realize a larger reflection for out-
+of-phase scenario, we use an optimization algorithm to
+search for an optimum solution of grid impedance profile
+and substrate thickness, which is powerful when many
+degrees of freedom are required in multi-channel meta-
+surface design. In the other design methodologies such as
+non-local metasurface [37] and plasmonic grating [23, 48],
+where the interference between all the elements of a unit
+cell are important for the device performance, a brute-
+force optimization process in full-wave simulations is re-
+quired, which is time consuming and even cannot work
+when multiple input beams and multi-functionalities for
+multiple channels are involved.
+Compared with them,
+our approach is much more robust and efficient due to
+a rigorous theoretical analysis, particularly by introduc-
+ing unidirectional evanescent mode in the scattered field
+to eliminate parasitic reflections. Moreover, the angle-
+dependence of the impedance of substrate is also con-
+sidered in our algorithm, which is vital in metasurface
+design for multiple-angle incidence scenarios [49, 50].
+We have realized a gradient metasurface with angular-
+asymmetric coherent perfect absorption and reflection
+functionalities. The concept of wave control via evanes-
+cent harmonics engineering and independent control of
+the electromagnetic response for multiple illuminations
+can be applied for engineering multi-functional wave pro-
+cesses. Metasurface-based designs are attractive in prac-
+tical applications.
+For example, by placing a planar
+structure on a metal-grounded dielectric layer, the veloc-
+ity or position of the object can be detected by monitor-
+
+10
+ing the total reflection of such a object under two coher-
+ent illuminations. Additionally, we hope that this work
+can find promising applications in phased-array anten-
+nas, one-side detection and sensing, and optical switches
+with low insertion loss.
+VI.
+METHODS
+Design and modeling of the metasurface
+The prototype presented in this work was designed
+for operation at 15.22 GHz. The grid impedance is dis-
+cretized into 6 sub-cells, and each sub-cell is divided into
+4 equal sub-sub-cells.
+The effective grid impedance of
+each sub-sub-cell is retrieved from simulated reflection
+coefficient (S11) through the transmission-line method
+approach (see the Supplementary Material[43]). Numeri-
+cal simulations are carried out using a frequency-domain
+solver, implemented by CST MWS. Excitations propa-
+gating along the z-direction from port 1 with the electric
+field along the y-direction and the magnetic field along
+the x-direction are used in the simulations to obtain the
+S11 parameter. The dimensions of all the elements in the
+unit cells are designed and optimized one by one to fit
+the theoretically found required surface impedance.
+Once the dimensions of all the elements in the unit
+cells are found, we perform numerical simulations of the
+unit cell in CST MWS for the normal and 45◦ incidences.
+The simulation domain of the complete unit cell was D×
+Dy × D (along the x, y, and z directions), the unit cell
+boundary condition and the Floquet port were set. The
+scattered fields for the normal and 45◦ incidences were
+calculated by subtracting the incident waves from the
+total fields. Finally, the total scattered fields when the
+metasurface is illuminated by two waves silmutaneously
+were obtained by adding the scattered field of each single
+beam with different phase differences.
+Realization and measurement
+The ITO pattern of the metasurface was manufactured
+using the picosecond laser micromachining technology on
+a 0.175-mm-thick ITO/PET film. The sample comprises
+10 unit cells along the x axis and 66 unit cells along the
+y axis [Fig. 5(b)] and has the size of 14.15λ × 10.04λ =
+278.9 mm × 198 mm. The ITO/PET film was adhered
+to a 4.95-mm-thick F4BTM substrate with ϵ = 5.8(1 −
+j0.01) backed by a copper ground plane.
+The operation of the designed metasurface was tested
+using a NRL-arc setup [Fig.
+5(b)]. In the experiment,
+two double-ridged horn antennas with 17 dBi gain at
+15.22 GHz are connected to a vector network analyzer
+as the transmitter and receiver. The metasurface was lo-
+cated at a distance of 2 m (about 101λ) from both the
+transmitting and receiving antennas where the radiation
+from the antenna can be approximated as a plane wave.
+The antennas are moved along the scanning track to mea-
+sure the reflection towards different angles. Time gating
+is employed to filter out all the multiple scattering noise
+signals received by the antenna [43].
+VII.
+DATA AVAILABILITY
+The data that support the findings of this study are
+available from the corresponding authors upon reason-
+able request.
+[1] Fu, Y. et al. All-optical logic gates based on nanoscale
+plasmonic slot waveguides.
+Nano Lett. 12, 5784–5790
+(2012).
+[2] Fang, X. et al. Ultrafast all-optical switching via coher-
+ent modulation of metamaterial absorption. Appl. Phys.
+Lett. 104, 141102 (2014).
+[3] Shi, J. et al. Coherent control of snell’s law at metasur-
+faces. Opt. Express 22, 21051–21060 (2014).
+[4] Papaioannou, M., Plum, E., Valente, J., Rogers, E. T.
+& Zheludev, N. I. Two-dimensional control of light with
+light on metasurfaces. Light: Sci. Appl. 5, e16070 (2016).
+[5] Papaioannou, M., Plum, E., Valente, J., Rogers, E. T. &
+Zheludev, N. I. All-optical multichannel logic based on
+coherent perfect absorption in a plasmonic metamaterial.
+APL Photonics 1, 090801 (2016).
+[6] Fang, X., MacDonald, K. F. & Zheludev, N. I.
+Con-
+trolling light with light using coherent metadevices: all-
+optical transistor, summator and invertor.
+Light: Sci.
+Appl. 4, e292–e292 (2015).
+[7] Silva, A. et al. Performing mathematical operations with
+metamaterials. Science 343, 160–163 (2014).
+[8] Achouri, K., Lavigne, G., Salem, M. A. & Caloz, C.
+Metasurface spatial processor for electromagnetic remote
+control. IEEE Trans. Antennas Propag. 64, 1759–1767
+(2016).
+[9] Zhu, Z., Yuan, J. & Jiang, L. Multifunctional and mul-
+tichannel all-optical logic gates based on the in-plane co-
+herent control of localized surface plasmons. Opt. Lett.
+45, 6362–6365 (2020).
+[10] Kang, M. et al. Coherent full polarization control based
+on bound states in the continuum. Nat. Commun. 13,
+1–9 (2022).
+[11] Peng, P. et al.
+Coherent control of ultrafast extreme
+ultraviolet transient absorption. Nat. Photonics 16, 45–
+51 (2022).
+[12] Chong, Y. D., Ge, L., Cao, H. & Stone, A. D. Coherent
+perfect absorbers: Time-reversed lasers. Phys. Rev. Lett.
+105, 053901 (2010).
+[13] Wan, W., Chong, Y., Li Ge, H. N., Stone, A. D. & Cao,
+H. Time-reversed lasing and interferometric control of
+absorption. Science 331, 889–892 (2011).
+[14] Dutta-Gupta, S., Deshmukh, R., Gopal, A. V., Martin,
+O. J. F. & Gupta, S. D.
+Coherent perfect absorption
+mediated anomalous reflection and refraction. Opt. Lett.
+37, 4452–4454 (2012).
+[15] Baranov, D. G., Krasnok, A., Shegai, T., Al`u, A. &
+Chong, Y.
+Coherent perfect absorbers: linear control
+of light with light. Nat. Rev. Mater. 2, 17064 (2017).
+
+11
+[16] Pirruccio, G., Ramezani, M., Rodriguez, S. R.-K. & Ri-
+vas, J. G. Coherent control of the optical absorption in
+a plasmonic lattice coupled to a luminescent layer. Phys.
+Rev. Lett. 116, 103002 (2016).
+[17] Jung, M. J., Han, C., Yoon, J. W. & Song, S. H. Tem-
+perature and gain tuning of plasmonic coherent perfect
+absorbers. Opt. Express 23, 19837–19845 (2015).
+[18] Yoon, J. W., Jung, M. J. & Song, S. H. Gain-assisted
+critical coupling for high-performance coherent perfect
+absorbers. Opt. Lett. 40, 2309–2312 (2015).
+[19] Kita, S. et al. Coherent control of high efficiency metasur-
+face beam deflectors with a back partial reflector. APL
+Photonics 2, 046104 (2017).
+[20] Xomalis, A. et al. Fibre-optic metadevice for all-optical
+signal modulation based on coherent absorption.
+Nat.
+Commun. 9, 182 (2018).
+[21] Wang, C., Sweeney, W. R., Stone, A. D. & Yang, L. Co-
+herent perfect absorption at an exceptional point. Science
+373, 1261–1265 (2021).
+[22] Li, S. et al. Broadband perfect absorption of ultrathin
+conductive films with coherent illumination: Superab-
+sorption of microwave radiation. Phys. Rev. B 91, 220301
+(2015).
+[23] Yoon, J. W., Koh, G. M., Song, S. H. & Magnusson,
+R.
+Measurement and modeling of a complete optical
+absorption and scattering by coherent surface plasmon-
+polariton excitation using a silver thin-film grating. Phys.
+Rev. Lett. 109, 257402 (2012).
+[24] Zhang, W. & Zhang, X. Backscattering-immune comput-
+ing of spatial differentiation by nonreciprocal plasmonics.
+Phys. Rev. Applied 11, 054033 (2019).
+[25] Yu, N. et al. Light propagation with phase discontinu-
+ities: generalized laws of reflection and refraction. science
+334, 333–337 (2011).
+[26] Sun, S. et al. Gradient-index meta-surfaces as a bridge
+linking propagating waves and surface waves. Nat. Mater.
+11, 426–431 (2012).
+[27] Kildishev, A. V., Boltasseva, A. & Shalaev, V. M. Pla-
+nar photonics with metasurfaces. Science 339, 1232009
+(2013).
+[28] Epstein, A. & Eleftheriades, G. V. Synthesis of passive
+lossless metasurfaces using auxiliary fields for reflection-
+less beam splitting and perfect reflection. Physical review
+letters 117, 256103 (2016).
+[29] Ra’di, Y., Sounas, D. L. & Al`u, A. Metagratings: Beyond
+the limits of graded metasurfaces for wave front control.
+Phys. Rev. Lett. 119, 067404 (2017).
+[30] Epstein, A. & Rabinovich, O. Unveiling the properties of
+metagratings via a detailed analytical model for synthesis
+and analysis. Physical Review Applied 8, 054037 (2017).
+[31] Popov, V., Boust, F. & Burokur, S. N.
+Controlling
+diffraction patterns with metagratings. Physical Review
+Applied 10, 011002 (2018).
+[32] Wong, A. M. & Eleftheriades, G. V. Perfect anomalous
+reflection with a bipartite huygens’ metasurface. Physical
+Review X 8, 011036 (2018).
+[33] Cao, Y. et al.
+Mechanism behind angularly asymmet-
+ric diffraction in phase-gradient metasurfaces. Physical
+Review Applied 12, 024006 (2019).
+[34] Fu, Y. et al. Reversal of transmission and reflection based
+on acoustic metagratings with integer parity design. Na-
+ture Commun. 10, 1–8 (2019).
+[35] Zhang, Z. et al. Coherent perfect diffraction in metagrat-
+ings. Adv. Mater. 32, 2002341 (2020).
+[36] Sun, S. et al. High-efficiency broadband anomalous reflec-
+tion by gradient meta-surfaces. Nano Lett. 12, 6223–6229
+(2012).
+[37] D´ıaz-Rubio, A., Asadchy, V. S., Elsakka, A. & Tretyakov,
+S. A.
+From the generalized reflection law to the re-
+alization of perfect anomalous reflectors.
+Sci. Adv. 3,
+e1602714 (2017).
+[38] He, T. et al. Perfect anomalous reflectors at optical fre-
+quencies. Science advances 8, eabk3381 (2022).
+[39] Cuesta, F., Ptitcyn, G., Mirmoosa, M. & Tretyakov, S.
+Coherent retroreflective metasurfaces.
+Phys. Rev. Re-
+search 3, L032025 (2021).
+[40] Cuesta, F., Kuznetsov, A., Ptitcyn, G., Wang, X. &
+Tretyakov, S.
+Coherent asymmetric absorbers.
+Phys.
+Rev. Applied 17, 024066 (2022).
+[41] Wang, X. et al. Extreme asymmetry in metasurfaces via
+evanescent fields engineering: Angular-asymmetric ab-
+sorption. Phys. Rev. Lett. 121, 256802 (2018).
+[42] Wang, X., D´ıaz-Rubio, A. & Tretyakov, S. A. Indepen-
+dent control of multiple channels in metasurface devices.
+Phys. Rev. Applied 14, 024089 (2020).
+[43] See Supplemental Material for additional information.
+[44] Hwang, R.-B.
+Periodic structures: mode-matching ap-
+proach and applications in electromagnetic engineering
+(John Wiley & Sons, 2012).
+[45] Zhirihin, D., Simovski, C., Belov, P. & Glybovski, S.
+Mushroom high-impedance metasurfaces for perfect ab-
+sorption at two angles of incidence.
+IEEE Antennas
+Wireless Propag. Lett. 16, 2626–2629 (2017).
+[46] Wang, X., Asadchy, V. S., Fan, S. & Tretyakov, S. A.
+Space–time metasurfaces for power combining of waves.
+ACS Photonics 8, 3034–3041 (2021).
+[47] Luukkonen, O. et al.
+Simple and accurate analytical
+model of planar grids and high-impedance surfaces com-
+prising metal strips or patches. IEEE Trans. Antennas
+Propag. 56, 1624–1632 (2008).
+[48] Chen, X. et al. Broadband janus scattering from tilted
+dipolar metagratings. Laser Photonics Rev. 16, 2100369
+(2022).
+[49] Zhang, X. et al. Controlling angular dispersions in optical
+metasurfaces. Light Sci. Appl. 9, 1–12 (2020).
+[50] Yuan, Y., Cheng, J., Fan, F., Wang, X. & Chang, S. Con-
+trol of angular dispersion in dielectric gratings for mul-
+tifunctional wavefront shaping and dynamic polarization
+conversion. Photonics Res. 9, 2190–2195 (2021).
+VIII.
+ACKNOWLEDGEMENTS
+The authors are grateful to Dr. Viktar S. Asadchy for
+useful discussions.
+S.M.Z. acknowledges support from
+China Scholarship Council. This research was also sup-
+ported by the Natural Science Foundation of Zhejiang
+Province(LY22F010001), the Natural Science Founda-
+tion of China (61701268), and the Fundamental Research
+Funds for the Provincial Universities of Zhejiang.
+IX.
+AUTHOR CONTRIBUTIONS
+S.M.Z. and X.C.W. conceived the study. S.M.Z. per-
+formed the numerical calculations, and designed the sam-
+
+12
+ples. S.M.Z. conducted the experiment. S.M.Z., X.C.W.,
+and S.A.T. wrote the paper.
+S.A.T. supervised the
+project. All authors contributed to scientific discussions
+and editing the manuscript.
+X.
+COMPETING INTERESTS
+The authors declare no competing interests.
+XI.
+ADDITIONAL INFORMATION
+Supplementary information The online version
+contains supplementary material available at https:xxxx.
+Correspondence and requests for materials should
+be addressed to Shuomin Zhong or Xuchen Wang.
+

6NAyT4oBgHgl3EQfpfik/content/tmp_files/2301.00527v1.pdf.txt

@@ -0,0 +1,775 @@
+Diffusion Probabilistic Models for Scene-Scale 3D Categorical Data
+Jumin Lee
+Woobin Im
+Sebin Lee
+Sung-Eui Yoon
+Korea Advanced Institute of Science and Technology (KAIST)
+{jmlee,iwbn,seb.lee,sungeui}@kaist.ac.kr
+Abstract
+In this paper, we learn a diffusion model to generate
+3D data on a scene-scale. Specifically, our model crafts a
+3D scene consisting of multiple objects, while recent diffu-
+sion research has focused on a single object. To realize our
+goal, we represent a scene with discrete class labels, i.e.,
+categorical distribution, to assign multiple objects into se-
+mantic categories. Thus, we extend discrete diffusion mod-
+els to learn scene-scale categorical distributions. In addi-
+tion, we validate that a latent diffusion model can reduce
+computation costs for training and deploying. To the best
+of our knowledge, our work is the first to apply discrete
+and latent diffusion for 3D categorical data on a scene-
+scale. We further propose to perform semantic scene com-
+pletion (SSC) by learning a conditional distribution using
+our diffusion model, where the condition is a partial ob-
+servation in a sparse point cloud. In experiments, we em-
+pirically show that our diffusion models not only generate
+reasonable scenes, but also perform the scene completion
+task better than a discriminative model. Our code and mod-
+els are available at https://github.com/zoomin-
+lee/scene-scale-diffusion.
+1. Introduction
+Learning to generate 3D data has received much atten-
+tion thanks to its high performance and promising down-
+stream tasks. For instance, a 3D generative model with a
+diffusion probabilistic model [2] has shown its effectiveness
+in 3D completion [2] and text-to-3D generation [1,3].
+While recent models have focused on 3D object gener-
+ation, we aim beyond a single object by generating a 3D
+scene with multiple objects. In Fig. 1b, we show a sam-
+ple scene from our generative model, where we observe the
+plausible placement of the objects, as well as their correct
+shapes. Compared to the existing object-scale model [1]
+(Fig. 1a), our scene-scale model can be used in a broader
+application, such as semantic scene completion (Sec. 4.3),
+where we complete a scene given a sparse LiDAR point
+6
+Pedestrian
+Building
+Vegetation
+Vehicle
+Diffusion 
+Model
+(a) Object-scale generation
+6
+Diffusion 
+Model
+6
+(b) Scene-scale generation (ours)
+Figure 1. Comparison of object-scale and scene scale generation
+(ours). Our result includes multiple objects in a generated scene,
+while the object-scale generation crafts one object at a time. (a) is
+obtained by Point-E [1].
+cloud.
+We base our scene-scale 3D generation method on a dif-
+fusion model, which has shown remarkable performance in
+modeling complex real-world data, such as realistic 2D im-
+ages [4–6] and 3D objects [1–3]. We develop and evaluate
+diffusion models learning a scene-scale 3D categorical dis-
+tribution.
+First, we utilize categorical data for a voxel entity since
+we have multiple objects in contrast to the existing work [1–
+3], so each category tells each voxel belongs to which cat-
+egory. Thus, we extend discrete diffusion models for 2D
+categorical data [7, 8] into 3D categorical data (Sec. 3.1).
+Second, we validate the latent diffusion model for the 3D
+scene-scale generation, which can reduce training and test-
+ing computational cost (Sec. 3.2). Third, we propose to per-
+form semantic scene completion (SSC) by learning a con-
+ditional distribution using our generative models, where the
+condition is a partial observation of the scene (Sec. 3.1).
+That is, we demonstrate that our model can complete a rea-
+arXiv:2301.00527v1  [cs.CV]  2 Jan 2023
+
+Building
+Barrier
+Other
+Pedestrian
+Pole
+Road
+Ground
+Sidewalk
+Vegetation
+Vehiclessonable scene in a realistic scenario with a sparse and partial
+observation.
+Lastly, we show the effectiveness of our method in terms
+of the unconditional and conditional (SSC) generation tasks
+on the CarlaSC dataset [9] (Sec. 4). Especially, we show
+that our generative model can outperform a discriminative
+model in the SSC task.
+2. Related Work
+2.1. Semantic Scene Completion
+Leveraging 3D data for semantic segmentation has been
+studied from different perspectives. Vision sensors (e.g.,
+RGB-D camera and LiDAR) provide depth information
+from a single viewpoint, giving more information about the
+world. One of the early approaches is using an RGB-D (i.e.,
+color and depth) image with a 2D segmentation map [10].
+In addition, using data in a 3D coordinate system has been
+extensively studied. 3D semantic segmentation is the exten-
+sion of 2D segmentation, where a classifier is applied to
+point clouds or voxel data in 3D coordinates [11,12].
+One of the recent advances in 3D semantic segmentation
+is semantic scene completion (SSC), where a partially ob-
+servable space – observed via RGB-D image or point clouds
+– should be densely filled with class labels [13–16]. In SSC,
+a model gets the point cloud obtained in one viewpoint;
+thus, it contains multiple partial objects (e.g., one side of a
+car). Then, the model not only reconstructs the unobserved
+shape of the car but also labels it as a car. Here, the predic-
+tion about the occupancy and the semantic labels can mutu-
+ally benefit [17].
+Due to the partial observation, filling in occluded and
+sparse areas is the biggest hurdle. Thus, a generative model
+is effective for 3D scene completion as 2D completion
+tasks [18, 19]. Chen et al. [20] demonstrate that generative
+adversarial networks (GANs) can be used to improve the
+plausibility of a completion result. However, a diffusion-
+based generative model has yet to be explored in terms of
+a 3D semantic segmentation map. We speculate that us-
+ing a diffusion model has good prospects, thanks to the
+larger size of the latent and the capability to deal with high-
+dimensional data.
+In this work, we explore a diffusion model in the context
+of 3D semantic scene completion. Diffusion models have
+been rapidly growing and they perform remarkably well on
+real-world 2D images [21]. Thus, we would like to delve
+into the diffusion to generate 3D semantic segmentation
+maps; thus, we hope to provide the research community a
+useful road map towards generating the 3D semantic scene
+maps.
+2.2. Diffusion Models
+Recent advances in diffusion models have shown that a
+deep model can learn more diverse data distribution by a
+diffusion process [5]. A diffusion process is introduced to
+adopt a simple distribution (e.g., Gaussian) to learn a com-
+plex distribution [4]. Especially, diffusion models show im-
+pressive results for image generation [6] and conditional
+generation [22, 23] on high resolution compared to GANs.
+GANs are known to suffer from the mode collapse prob-
+lem and struggle to capture complex scenes with multiple
+objects [24]. On the other hand, diffusion models have a ca-
+pacity to escape mode collapse [6] and generate complex
+scenes [23,25] since likelihood-based methods achieve bet-
+ter coverage of full data distribution.
+Diffusion models have been studied to a large extent in
+high-dimensional continuous data. However, they often lack
+the capacity to deal with discrete data (e.g., text and seg-
+mentation maps) since the discreteness of data is not fully
+covered by continuous representations. To tackle such dis-
+creteness, discrete diffusion models have been studied for
+various applications, such as text generation [7,8] and low-
+dimensional segmentation maps generation [7].
+Since both continuous and discrete diffusion models es-
+timate the density of image pixels, a higher image res-
+olution means higher computation. To address this issue,
+latent diffusion models [23, 26] operate a diffusion pro-
+cess on the latent space of a lower dimension. To work
+on the compressed latent space, Vector-Quantized Varia-
+tional Auto-Encoder (VQ-VAE) [27] is employed. Latent
+diffusion models consist of two stages: VQ-VAE and dif-
+fusion. VQ-VAE trains an encoder to compress the image
+into a latent space. Equipped with VQ-VAE, autoregressive
+models [28, 29] have shown impressive performance. Re-
+cent advances in latent diffusion models further improve
+the generative performance by ameliorating the unidirec-
+tional bias and accumulated prediction error in existing
+models [23,26].
+Our work introduces an extension of discrete diffu-
+sion models for high-resolution 3D categorical voxel data.
+Specifically, we show the effectiveness of a diffusion model
+in terms of unconditional and conditional generation tasks,
+where the condition is a partial observation of a scene (i.e.,
+SSC). Further, we propose a latent diffusion models for 3D
+categorical data to reduce the computation load caused by
+high-resolution segmentation maps.
+2.3. Diffusion Models for 3D Data
+Diffusion models have been used for 3D data. Until re-
+cently, research has been mainly conducted for 3D point
+clouds with xyz-coordinates. PVD [2] applies continuous
+diffusion on point-voxel representations for object shape
+generation and completion without additional shape en-
+coders. LION [3] uses latent diffusion for object shape com-
+
+Forward Process
+Reverse Process
+(a) Discrete Diffusion Models
+Segmentation Map
+Segmentation Map
+Reverse Process
+Codebook
+Stage1:VQ-VAE
+Stage2: Latent Diffusion 
+Forward Process
+(b) Latent Diffusion Models
+Figure 2. Overview of (a) Discrete Diffusion Models and (b) La-
+tent Diffusion Models. Discrete diffusion models conduct diffu-
+sion process on voxel space, whereas latent diffusion models op-
+erate diffusion process on latent space.
+pletion (i.e., conditional generation) with additional shape
+encoders.
+In this paper, we aim to learn 3D categorical data (i.e.,
+3D semantic segmentation maps) with a diffusion model.
+The study of object generation has shown promising re-
+sults, but as far as we know, our work is the first to generate
+a 3D scene with multiple objects using a diffusion model.
+Concretely, our work explores discrete and latent diffusion
+models to learn a distribution of volumetric semantic scene
+segmentation maps. We develop the models in an uncon-
+ditional and conditional generation; the latter can be used
+directly for the SSC task.
+3. Method
+Our goal is to learn a data distribution p(x) using dif-
+fusion models, where each data x ∼ p(x) represents a
+3D segmentation map described with the one-hot repre-
+sentation. 3D segmentation maps are samples from the
+data distribution p(x), which is the categorical distribution
+Cat(k0, k1, · · · , kM) with M +1 probabilities of the free la-
+bel k0 and M main categories. The discrete diffusion mod-
+els could learn data distribution by recovering the noised
+data, which is destroyed through the successive transition
+of the label [8].
+Our method aims to learn a distribution of voxelized
+3D segmentation maps with discrete diffusion (Sec. 3.1).
+Specifically, it includes unconditional and conditional gen-
+eration, where the latter corresponds to the SSC task. In ad-
+dition, we explore a latent diffusion model for 3D segmen-
+tation maps (Sec. 3.2).
+3.1. Discrete Diffusion Models
+Fig. 2a summarizes the overall process of discrete diffu-
+sion, consisting of a forward process and a reverse process;
+the former gradually adds noise to the data and the latter
+learns to denoise the noised data.
+In the forward process in the discrete diffusion, an origi-
+nal segmentation map x0 is gradually corrupted into a t-step
+noised segmentation map xt with 1 ≤ t ≤ T. Each forward
+step can be defined by a Markov uniform transition matrix
+Qt [8] as xt = xt−1Qt. Based on the Markov property, we
+can derive the t-step noised segmentation map xt straight
+from the original segmentation map x0, q(xt|x0), with a
+cumulative transition matrix ¯Qt = Q1Q2 · · · Qt:
+q(xt|x0) = Cat(xt; p = x0 ¯Qt).
+(1)
+In the reverse process parametrized by θ, a learn-
+able model is used to reverse a noised segmentation map
+by pθ(xt−1|xt). Specifically, we use a reparametrization
+trick [5] to make the model predict a denoised map ˜x0 and
+subsequently get the reverse process pθ(xt−1|xt):
+pθ(xt−1|xt) = q(xt−1|xt, ˜x0)pθ(˜x0|xt),
+(2)
+q(xt−1|xt, ˜x0) = q(xt|xt−1, ˜x0)q(xt−1|˜x0)
+q(xt|˜x0)
+.
+(3)
+We optimize a joint loss that consists of the KL di-
+vergence of the forward process q(xt−1|xt, x0) from the
+reverse process pθ(xt−1|xt); of the original segmentation
+map q(x0) from the reconstructed one pθ(xt−1|xt) for an
+auxiliary loss:
+L = DKL( q(xt−1|xt, x0) ∥ pθ(xt−1|xt) )
++ w0DKL( q(x0) ∥ pθ(˜x0|xt) ),
+(4)
+where w0 is an auxiliary loss weight.
+Unlike existing discrete diffusion models [7,8], our goal
+is to learn the distribution of 3D data. Thus, to better handle
+3D data, we use a point cloud segmentation network [30]
+with modifications for discrete data and time embedding.
+Conditional generation.
+We propose discrete diffusion
+for Semantic Scene Completion (SSC) with conditional
+generation. SSC jointly estimates a scene’s complete geom-
+etry and semantics, given a sparse occupancy map s. Thus,
+it introduces a condition into Eq. 2, resulting in:
+pθ(xt−1|xt, s) = q(xt−1|xt, ˜x0)pθ(˜x0|xt, s),
+(5)
+
+where s is a sparse occupancy map. We give the condition
+by concatenating a sparse occupancy map s with a corrupted
+input xt.
+3.2. Latent Diffusion Models
+Fig. 2b provides an overview of latent diffusion on 3D
+segmentation maps. Latent diffusion models project the 3D
+segmentation maps into a smaller latent space and operate
+a diffusion process on the latent space instead of the high-
+dimensional input space. A latent diffusion takes advantage
+of a lower training computational cost and a faster inference
+by processing diffusion on a lower dimensional space.
+To encode a 3D segmentation map into a latent rep-
+resentation, we use Vector Quantized Variational AutoEn-
+coder (VQ-VAE) [27]. VQ-VAE extends the VAE by adding
+a discrete learnable codebook E = {en}N
+n=1 ∈ RN×d,
+where N is the size of the codebook and d is the dimension
+of the codes. The encoder E encodes 3D segmentation maps
+x into a latent z = E(x), and the quantizer V Q(·) maps
+the latent z into a quantized latent zq, which is the closest
+codebook entry en. Note that the latent z ∈ Rh×w×z×d has
+a smaller spatial resolution than the segmentation map x.
+Then the decoder D reconstructs the 3D segmentation maps
+from the quantized latent, ˜x = D(V Q(E(x))). The encoder
+E, the decoder D, and the codebook E can be trained end-
+to-end using the following loss function:
+LV QV AE = −
+�
+k
+wkxk log(˜xk) + ∥sg(z) − zq∥2
+2
++ ∥z − sg(zq)∥2
+2,
+(6)
+where wk is a class weight and sg(·) is the stop-gradient
+operation. Training the latent diffusion model is similar to
+that of discrete diffusion. Discrete diffusion models diffuse
+between labels, but latent diffusion models diffuse between
+codebook indexes using Markov Uniform transition matrix
+Qt [8].
+4. Experiments
+In this section, we empirically study the effectiveness of
+the diffusion models on 3D voxel segmentation maps. We
+divide the following sub-sections into the learning of the
+unconditional data distribution p(x) (Sec. 4.2) and the con-
+ditional data distribution p(x|s) given a sparse occupancy
+map s (Sec. 4.3); note that the latter corresponds to seman-
+tic scene completion (SSC).
+4.1. Implementation Details
+Dataset. Following prior work [9], we employ the CarlaSC
+dataset – a synthetic outdoor driving dataset – for training
+and evaluation. The dataset consists of 24 scenes in 8 dy-
+namic maps under low, medium, and high traffic conditions.
+Model
+Resolution
+Training
+(time/epoch)
+Sampling
+(time/img)
+D-Diffusion
+128×128×8
+19m 48s
+0.883s
+L-Diffusion
+32×32×2
+7m 37s
+0.499s
+16×16×2
+4m 41s
+0.230s
+8×8×2
+4m 40s
+0.202s
+Table 1. Computation time comparison between discrete diffu-
+sion models and latent diffusion models for 3D segmentation maps
+generation. ‘D-Diffusion’ and ‘L-Diffusion’ denote discrete diffu-
+sion models and latent diffusion models, respectively. ‘Resolution’
+means the resolution of the space in which diffusion process op-
+erates. A latent diffusion models process diffusion on a lower di-
+mensional latent space, as a result, it shows advantage of a faster
+training and sampling time.
+The splits of the dataset contain 18 training, 3 validation,
+and 3 test scenes, which are annotated with 10 semantic
+classes and a free label. Each scene with a resolution of
+128 × 128 × 8 covers a range of 25.6 m ahead and behind
+the car, 25.6 m to each side, and 3 m in height.
+Metrics. Since SSC requires predicting the semantic label
+of a voxel and an occupancy state together, we use mIoU
+and IoU as SSC and VQ-VAE metrics. The mIoU measures
+the intersection over union averaged over all classes, and
+the IoU evaluates scene completion quality, regardless of
+the predicted semantic labels.
+Experimental settings. Experiments are deployed on two
+NVIDIA GTX 3090 GPUs with a batch size of 8 for dif-
+fusion models and 4 for VQ-VAE. Our models follow the
+same training strategy as multinomial diffusion [7]. We set
+the hyper-parameters of the diffusion models with the num-
+ber of time steps T = 100 timesteps. And for VQ-VAE,
+we set the codebook E = {en}N
+n=1 ∈ RN×d where the
+codebook size N = 1100, dimension of codes d = 11 and
+en ∈ R32×32×2×d. For diffusion architecture, we slightly
+modify the encoder–decoder structure in Cylinder3D [30]
+for time embedding and discreteness of the data. And for
+VQ-VAE architecture, we also use encoder–decoder struc-
+ture in Cylinder3D [30], but with the vector quantizer mod-
+ule.
+4.2. 3D Segmentation Maps Generation
+We use the discrete and the latent diffusion models for
+3D segmentation map generation. Fig. 3 shows the quali-
+tative results of the generation. As seen in the figure, both
+the discrete and latent models learn the categorical distri-
+bution as they produce a variety of reasonable scenes. Note
+that our models are learned on a large-scale data distribution
+like the 3D scene with multiple objects; this is worth noting
+since recent 3D diffusion models for point clouds have been
+performed on an object scale [2,3,31,32].
+In Tab. 1, we compare training and sampling time mod-
+
+Codebook size
+(N)
+Resolution
+(h × w × z)
+IoU
+mIoU
+220
+8×8×2
+72.5
+27.3
+16×16×2
+78.7
+36.9
+32×32×2
+84.6
+56.5
+550
+8×8×2
+67.7
+25.7
+16×16×2
+79.4
+39.7
+32×32×2
+85.8
+58.4
+1,100
+8×8×2
+70.3
+25.7
+16×16×2
+79.3
+35.0
+32×32×2
+89.1
+65.1
+2,200
+8×8×2
+70.2
+26.5
+16×16×2
+77.7
+37.9
+32×32×2
+89.2
+64.2
+Table 2. Ablation study on VQ-VAE hyper-parameters. We
+compare different sizes of codebook N and resolutions of the la-
+tent space h×w×z.
+els for different resolutions on which each diffusion model
+operates. Compared to the discrete diffusion, the latent dif-
+fusion tends to show shorter training and inference time.
+This is because the latent diffusion models compress the
+data into a smaller latent so that the time decreases as the
+compression rate increases. In particular, compared to dis-
+crete diffusion, which performs a diffusion process in voxel
+space, 32 × 32 × 32 latent diffusion has 2.6 times faster
+training time for one epoch and 1.8 times faster sampling
+time for generating one image.
+Ablation study on VQ-VAE.
+Latent diffusion models
+consist of two stages. The VQ-VAE compresses 3D seg-
+mentation maps to latent space, and then discrete diffusion
+models apply on the codebook index of latent. Therefore,
+the performance of VQ-VAE may set the upper bound for
+the final generation quality. So we conduct an ablation study
+about VQ-VAE while adjusting the resolution of the latent
+space h×w×z and the codebook capacities N while keep-
+ing the code dimension d fixed. Concretely, we compress
+the 3D segmentation maps from 128×128×8 to 32×32×2,
+16×16×2, and 8×8×2 with four different codebook size
+N ∈ {220, 550, 1100, 2200}.
+The quantitative comparison is shown in Tab. 2. The big-
+ger the codebook size is, the higher the performance is, but
+it saturates around 1,100. That is because most of the codes
+are not updated, and the update of the codebook can lapse
+into a local optimum [33].
+The resolution of latent space has a significant impact on
+performance. As the resolution of the latent space becomes
+smaller, it cannot contain all the information of the 3D seg-
+mentation map. Setting the resolution to 32 × 32 × 2 with
+a 1,100 codebook size strike a good balance between effi-
+ciency and fidelity.
+Methods
+IoU
+mIoU
+LMSCNet SS [16]
+85.98
+42.53
+SSCNet Full [17]
+80.69
+41.91
+MotionSC (T=1) [9]
+86.46
+46.31
+Our network w/o Diffusion
+80.70
+39.94
+Discrete Diffusion (Ours)
+80.61
+45.83
+Table 3. Semantic Scene Completion results on test set of CarlaSC
+4.3. Semantic Scene Completion
+We use a discrete diffusion model for conditional 3D
+segmentation map generation (i.e., SSC). As a baseline
+model against the diffusion model, we train a network with
+an identical architecture by discriminative learning without
+a diffusion process. We optimize the baseline with a loss
+term L = − �
+k wkxk log(˜xk), where wk is a weight for
+each semantic class. We visualize results from the baseline
+and our discrete diffusion model in Fig. 4. Despite the com-
+plexities of the networks being identical, our discrete dif-
+fusion model improves mIoU (i.e., class-wise IoU) up to
+5.89%p than the baseline model as shown in Tab. 4. Es-
+pecially, our method achieves outstanding results in small
+objects and fewer frequency categories like ‘pedestrian’,
+‘pole’, ‘vehicles,’ and ‘other’. The qualitative results in
+Fig. 4 better demonstrate the improvement.
+In Tab. 3, we compare our model with existing SSC mod-
+els whose network architectures and training strategies are
+specifically built for the SSC task. Nonetheless, our diffu-
+sion model outperforms LMSCNet [16] and SSCNet [17],
+in spite of the simpler architecture and training strategies.
+Although MotionSC [9] shows a slightly better result, we
+speculate that the diffusion probabilistic model can be im-
+proved by extensive future research dedicated to this field.
+5. Conclusion
+In this work, we demonstrate the extension of the diffu-
+sion model to scene-scale 3D categorical data beyond gen-
+erating a single object. We empirically show that our mod-
+els have impressive generative power to craft various scenes
+through a discrete and latent diffusion process. Addition-
+ally, our method provides an alternative view for the SSC
+task, showing superior performance compared to a discrim-
+inative counterpart. We believe that our work can be a useful
+road map for generating 3D data with a diffusion model.
+References
+[1] A. Nichol, H. Jun, P. Dhariwal, P. Mishkin, and
+M. Chen, “Point-e: A system for generating 3d
+point clouds from complex prompts,” 2022. [Online].
+Available: https://arxiv.org/abs/2212.08751 1
+
+Training Datasets
+Latent Diffusion Models
+Discrete Diffusion Models
+Figure 3. Samples from our unconditional diffusion models. The first column shows samples from training datasets. From the second
+column, we show samples from our discrete diffusion and latent diffusion models. We can observe our diffusion models learn the 3D
+categorical distribution well, so that it is capable to generate a variety of plausible maps. Color assignment for each class is available in
+Tab. 4.
+Class IoU
+mIoU
+Free
+Building
+Barrier
+Other
+Pedestrian
+Pole
+Road
+Ground
+Sidewalk
+Vegetation
+Vehicles
+IoU
+w/o Diffusion
+39.94
+96.40
+27.72
+3.15
+8.77
+22.15
+37.14
+89.02
+18.22
+59.25
+29.74
+47.72
+80.70
+Discrete Diffusion (Ours)
+45.83
+96.00
+31.75
+3.42
+25.43
+46.22
+43.32
+84.57
+13.01
+67.50
+37.45
+55.46
+80.61
+Table 4. Semantic scene completion results on test set of CarlaSC. The discriminative learning result with the diffusion model architecture
+is denoted as ‘w/o Diffusion’. Values with a difference equal to or greater than 0.5%p are bold.
+Ground
+Truth
+Discrete 
+Diffusion 
+(ours)
+Input
+w/o 
+Diffusion 
+Figure 4. Qualitative comparison of a deterministic model (w/o diffusion) and ours (discrete diffusion) on the test split of CarlaSC.
+The first row shows the sparse inputs for the scene completion task, and the last row shows the corresponding ground-truth. Compared to
+the deterministic model, our probabilistic model produces more plausible shape and class inference, as highlighted by the red circles. Note
+that the both models (w/o diffusion and discrete diffusion) use the same network architecture. Color assignment for each class is available
+in Tab. 4.
+
+.X237[2] L. Zhou, Y. Du, and J. Wu, “3d shape generation
+and completion through point-voxel diffusion,” in Pro-
+ceedings of the IEEE/CVF International Conference
+on Computer Vision, 2021, pp. 5826–5835. 1, 2, 4
+[3] X. Zeng, A. Vahdat, F. Williams, Z. Gojcic, O. Litany,
+S. Fidler, and K. Kreis, “Lion: Latent point diffu-
+sion models for 3d shape generation,” arXiv preprint
+arXiv:2210.06978, 2022. 1, 2, 4
+[4] J. Sohl-Dickstein, E. Weiss, N. Maheswaranathan,
+and S. Ganguli, “Deep unsupervised learning using
+nonequilibrium thermodynamics,” in International
+Conference on Machine Learning.
+PMLR, 2015, pp.
+2256–2265. 1, 2
+[5] J. Ho, A. Jain, and P. Abbeel, “Denoising diffu-
+sion probabilistic models,” Advances in Neural Infor-
+mation Processing Systems, vol. 33, pp. 6840–6851,
+2020. 1, 2, 3
+[6] P. Dhariwal and A. Nichol, “Diffusion models beat
+gans on image synthesis,” Advances in Neural Infor-
+mation Processing Systems, vol. 34, pp. 8780–8794,
+2021. 1, 2
+[7] E. Hoogeboom, D. Nielsen, P. Jaini, P. Forr´e, and
+M. Welling, “Argmax flows and multinomial diffu-
+sion: Learning categorical distributions,” Advances in
+Neural Information Processing Systems, vol. 34, pp.
+12 454–12 465, 2021. 1, 2, 3, 4
+[8] J. Austin, D. D. Johnson, J. Ho, D. Tarlow, and
+R. van den Berg, “Structured denoising diffusion mod-
+els in discrete state-spaces,” Advances in Neural In-
+formation Processing Systems, vol. 34, pp. 17 981–
+17 993, 2021. 1, 2, 3, 4
+[9] J. Wilson, J. Song, Y. Fu, A. Zhang, A. Capodieci,
+P. Jayakumar, K. Barton, and M. Ghaffari, “Mo-
+tionsc: Data set and network for real-time semantic
+mapping in dynamic environments,” arXiv preprint
+arXiv:2203.07060, 2022. 2, 4, 5
+[10] J. Long, E. Shelhamer, and T. Darrell, “Fully convo-
+lutional networks for semantic segmentation,” in Pro-
+ceedings of the IEEE conference on computer vision
+and pattern recognition, 2015, pp. 3431–3440. 2
+[11] C. R. Qi, H. Su, K. Mo, and L. J. Guibas, “Pointnet:
+Deep learning on point sets for 3d classification and
+segmentation,” in Proceedings of the IEEE conference
+on computer vision and pattern recognition, 2017, pp.
+652–660. 2
+[12] G. Riegler, A. Osman Ulusoy, and A. Geiger, “Octnet:
+Learning deep 3d representations at high resolutions,”
+in Proceedings of the IEEE conference on computer
+vision and pattern recognition, 2017, pp. 3577–3586.
+2
+[13] R. Cheng, C. Agia, Y. Ren, X. Li, and L. Bingbing,
+“S3cnet: A sparse semantic scene completion network
+for lidar point clouds,” in Conference on Robot Learn-
+ing.
+PMLR, 2021, pp. 2148–2161. 2
+[14] X. Yan, J. Gao, J. Li, R. Zhang, Z. Li, R. Huang, and
+S. Cui, “Sparse single sweep lidar point cloud seg-
+mentation via learning contextual shape priors from
+scene completion,” in Proceedings of the AAAI Con-
+ference on Artificial Intelligence, vol. 35, no. 4, 2021,
+pp. 3101–3109. 2
+[15] C. B. Rist, D. Emmerichs, M. Enzweiler, and D. M.
+Gavrila, “Semantic scene completion using local deep
+implicit functions on lidar data,” IEEE transactions
+on pattern analysis and machine intelligence, vol. 44,
+no. 10, pp. 7205–7218, 2021. 2
+[16] L. Roldao, R. de Charette, and A. Verroust-Blondet,
+“Lmscnet: Lightweight multiscale 3d semantic com-
+pletion,” in 2020 International Conference on 3D Vi-
+sion (3DV).
+IEEE, 2020, pp. 111–119. 2, 5
+[17] S. Song, F. Yu, A. Zeng, A. X. Chang, M. Savva, and
+T. Funkhouser, “Semantic scene completion from a
+single depth image,” Proceedings of 30th IEEE Con-
+ference on Computer Vision and Pattern Recognition,
+2017. 2, 5
+[18] C. H. Jo, W. B. Im, and S.-E. Yoon, “In-n-out: Towards
+good initialization for inpainting and outpainting,” in
+The 32nd British Machine Vision Conference, BMVC
+2021.
+British Machine Vision Association (BMVA),
+2021. 2
+[19] A. Lugmayr, M. Danelljan, A. Romero, F. Yu, R. Tim-
+ofte, and L. Van Gool, “Repaint: Inpainting using de-
+noising diffusion probabilistic models,” in Proceed-
+ings of the IEEE/CVF Conference on Computer Vision
+and Pattern Recognition, 2022, pp. 11 461–11 471. 2
+[20] Y.-T. Chen, M. Garbade, and J. Gall, “3d semantic
+scene completion from a single depth image using ad-
+versarial training,” in 2019 IEEE International Con-
+ference on Image Processing (ICIP).
+IEEE, 2019,
+pp. 1835–1839. 2
+[21] A.
+Ramesh,
+P.
+Dhariwal,
+A.
+Nichol,
+C.
+Chu,
+and M. Chen, “Hierarchical text-conditional im-
+age generation with clip latents,” arXiv preprint
+arXiv:2204.06125, 2022. 2
+
+[22] C. Saharia, W. Chan, H. Chang, C. Lee, J. Ho, T. Sal-
+imans, D. Fleet, and M. Norouzi, “Palette: Image-to-
+image diffusion models,” in ACM SIGGRAPH 2022
+Conference Proceedings, 2022, pp. 1–10. 2
+[23] S. Gu, D. Chen, J. Bao, F. Wen, B. Zhang, D. Chen,
+L. Yuan, and B. Guo, “Vector quantized diffusion
+model for text-to-image synthesis,” in Proceedings of
+the IEEE/CVF Conference on Computer Vision and
+Pattern Recognition, 2022, pp. 10 696–10 706. 2
+[24] S.-H. Shim, S. Hyun, D. Bae, and J.-P. Heo, “Local at-
+tention pyramid for scene image generation,” in Pro-
+ceedings of the IEEE/CVF Conference on Computer
+Vision and Pattern Recognition, 2022, pp. 7774–7782.
+2
+[25] W.-C. Fan, Y.-C. Chen, D. Chen, Y. Cheng, L. Yuan,
+and Y.-C. F. Wang, “Frido: Feature pyramid diffusion
+for complex scene image synthesis,” arXiv preprint
+arXiv:2208.13753, 2022. 2
+[26] R. Rombach, A. Blattmann, D. Lorenz, P. Esser,
+and B. Ommer, “High-resolution image synthesis
+with latent diffusion models,” in Proceedings of the
+IEEE/CVF Conference on Computer Vision and Pat-
+tern Recognition, 2022, pp. 10 684–10 695. 2
+[27] A. Van Den Oord, O. Vinyals et al., “Neural discrete
+representation learning,” Advances in neural informa-
+tion processing systems, vol. 30, 2017. 2, 4
+[28] P. Esser, R. Rombach, and B. Ommer, “Taming trans-
+formers for high-resolution image synthesis,” in Pro-
+ceedings of the IEEE/CVF conference on computer
+vision and pattern recognition, 2021, pp. 12 873–
+12 883. 2
+[29] A. Ramesh, M. Pavlov, G. Goh, S. Gray, C. Voss,
+A. Radford, M. Chen, and I. Sutskever, “Zero-shot
+text-to-image generation,” in International Confer-
+ence on Machine Learning.
+PMLR, 2021, pp. 8821–
+8831. 2
+[30] X. Zhu, H. Zhou, T. Wang, F. Hong, Y. Ma, W. Li,
+H. Li, and D. Lin, “Cylindrical and asymmetrical 3d
+convolution networks for lidar segmentation,” in Pro-
+ceedings of the IEEE/CVF conference on computer vi-
+sion and pattern recognition, 2021, pp. 9939–9948. 3,
+4
+[31] M. Xu, L. Yu, Y. Song, C. Shi, S. Ermon, and
+J. Tang, “Geodiff: A geometric diffusion model for
+molecular conformation generation,” arXiv preprint
+arXiv:2203.02923, 2022. 4
+[32] S. Luo and W. Hu, “Diffusion probabilistic models
+for 3d point cloud generation,” in Proceedings of the
+IEEE/CVF Conference on Computer Vision and Pat-
+tern Recognition, 2021, pp. 2837–2845. 4
+[33] M. Hu, Y. Wang, T.-J. Cham, J. Yang, and P. N. Sug-
+anthan, “Global context with discrete diffusion in vec-
+tor quantised modelling for image generation,” in Pro-
+ceedings of the IEEE/CVF Conference on Computer
+Vision and Pattern Recognition, 2022, pp. 11 502–
+11 511. 5
+

79FLT4oBgHgl3EQfAy4h/vector_store/index.faiss

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:e34d98418330a49a45996f5e9a47e3f0daf9baef12c1eda46df8ae21dc14a630
+size 3538989

7tE4T4oBgHgl3EQf2g0r/content/2301.05298v1.pdf

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:aae5d96a289799346bfdf7ac4adda2649fe55f16616ccfa03e258f6499ac96ed
+size 1685470

7tE4T4oBgHgl3EQf2g0r/vector_store/index.faiss

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:5f65aa4ac05973f602a93bb4a1e2f619c0316ab22510b4aebdfa26a2be321cb4
+size 4653101

7tE4T4oBgHgl3EQf2g0r/vector_store/index.pkl

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:31ccb30ad750690d9d638e4353f175ec295f416a5dcb1bc0e7a9c515e4b12193
+size 194347

99AyT4oBgHgl3EQf3fke/content/tmp_files/2301.00768v1.pdf.txt

@@ -0,0 +1,2921 @@
+1 
+ 
+Ontology-based Context Aware Recommender System Application 
+for Tourism. 
+ 
+Vitor T. Camacho1, José Cruz2 
+1 PhD, [email protected], R&D Data Science, Syone. 
+2 MSc, [email protected], R&D Data Science, Syone. 
+ 
+Abstract 
+In this work a novel recommender system (RS) for Tourism is presented. The RS is context aware 
+as is now the rule in the state-of-the-art for recommender systems and works on top of a tourism 
+ontology which is used to group the different items being offered. The presented RS mixes 
+different types of recommenders creating an ensemble which changes on the basis of the RS’s 
+maturity. Starting from simple content-based recommendations and iteratively adding popularity, 
+demographic and collaborative filtering methods as rating density and user cardinality increases. 
+The result is a RS that mutates during its lifetime and uses a tourism ontology and natural 
+language processing (NLP) to correctly bin the items to specific item categories and meta 
+categories in the ontology. This item classification facilitates the association between user 
+preferences and items, as well as allowing to better classify and group the items being offered, 
+which in turn is particularly useful for context-aware filtering. 
+ 
+Keywords: recommender system, CARS, ontology, tourism, content-based, collaborative 
+filtering, demographic-based. 
+ 
+ 
+1 
+Introduction 
+This work presents a novel recommender system (RS) approach, which builds on context 
+awareness, domain ontology and different types of recommenders that enter the process at 
+different stages of maturity. From simple recommenders that are less prone to cold-start issues 
+to more complex and powerful recommenders which struggle quite a bit with initial lack of data. 
+At the final stage of maturity, when all the recommenders are already deployed in the 
+recommender pool, the different recommenders analyze different aspects of the data, from 
+demographic features to ratings, and provide an ensemble of recommendations to the users, 
+based on different approaches and with varying degrees of personalization. The approach is novel 
+
+2 
+ 
+in how it uses several techniques, from domain ontology to bin the items using NLP to achieve 
+concept similarity, and then from there applies content-based, demographic-based, popularity-
+based and collaborative filtering approaches to attain the recommended items. The collaborative 
+filtering employed are field-aware factorization machines which are the state-of-the-art in matrix 
+factorization, which can easily include context-awareness. The aim is to provide a powerful and 
+adaptable recommender system framework which can adapt to any domain, given the respective 
+domain ontology, and can overcome cold-start issues by using an approach with 4 stages of 
+maturity, which are subsequently entered when given thresholds are reached. In the following the 
+structure of the paper is presented, with an explanation of every section. In the present section, 
+the Introduction, an overview of the presented recommender system framework is provided as 
+well as a literature review of the relevant works on the subject. In section 2, the framework and 
+all its components are presented, from adopted technologies to used algorithms and techniques. 
+A presentation of the architecture is given as well as a mock-up of the designed UI to provide the 
+link between user and recommender system. In section 3, the technologies and techniques, 
+mainly the ones central to the recommender system are better explained with some formulas 
+being provided. In section 4, the recommender system is tested with a synthetic dataset with 
+varying stages of maturity, to show how the recommender system evolves as the data changes. 
+In section 5, conclusions are given as well as a brief discussion on future works. 
+ 
+1.1 
+Literature review 
+Recommender systems (RS) have been the focus of research for many years now, both on the 
+algorithm side and on the applied side. The study of RS started in the beginning of the 1990s but 
+it was in the last 15 years that research and the number of publications on the topic surged.  
+Concerning our application, tourism, RS have been the focus of studies since, at least, the start 
+of the 2000s with many publications having been made since then [1]–[15]. As for works that 
+concern more an algorithmic approach without an explicit thematic application, several studies 
+have been published on the different types of RS, from content-based approaches to collaborative 
+filtering, as well as context-aware solutions, so called CARS [16]–[64]. 
+Going into more detail regarding the tourism themed recommenders, it is relevant to give 
+particular attention to ontology-based approaches. One of the more important examples 
+concerning the present work is Moreno, A. et al. [8]. In this work, an ontology-based approach 
+(SigTur/E-destination) is developed to get recommendations for tourism in the region of 
+Tarragona. The developed approach begins with the definition of a tourism domain ontology, 
+which describes the tourist activities in a hierarchy, and bins the activities according to a given 
+taxonomy. The ontology is thus used to explicitly classify the activities to recommend among a 
+predefined set of distinctive main concepts, which are used by the intelligent recommender 
+system in its reasoning processes. The recommender than applies collaborative and content-
+based techniques to provide the recommendation. Another relevant work is that of García-
+Crespo, A. et al. [11], which proposes a semantic based expert system to provide 
+
+3 
+ 
+recommendations in the tourist domain (Sem-Fit). The proposed system works based on the 
+consumer’s experience about recommendations provided by the system. Sem-Fit uses the 
+experience point of view in order to apply fuzzy logic techniques to relating customer and hotel 
+characteristics, represented by means of domain ontologies and affect grids. An early and 
+interesting work that applies Bayesian networks to attain personalized recommendations for 
+tourist attractions by Huang, Y. and Bian, L. [15] is also worth mentioning. This work is from 2009 
+and uses ontologies to classify different types of tourist attractions. It then uses a Bayesian 
+network, to calculate the posterior probabilities of a given tourist’s preferred activities and the 
+traveler category he fits into. Other works on recommender system tourism applications could 
+also be mentioned but instead one can mention three surveys done on this topic. First, one from 
+2014, Borràs, J. et al. [2] present a survey entitled “Intelligent tourism recommender systems”. In 
+this survey the various works in the state-of-the-art are analyzed and their different approaches 
+concerning user interface, functionalities, recommendation techniques and use of AI techniques 
+are presented. The second work that gives an overview on the topic is from Kzaz, L. et al. [3] from 
+2018. In this overview, the focus is essentially on recommender approaches and employed user 
+and item data models. A third survey on this topic is given to us by Renjith, S. et al. [60] in a work 
+titled “An extensive study on the evolution of context-aware personalized travel recommender 
+systems”. Herein, the authors start by defining the different recommender approaches that can 
+be employed: content-based, collaborative, demographic-based, knowledge-based, hybrid, 
+personalized and context-aware. The authors also go into detail on the different machine learning 
+algorithms that are commonly employed, as well as the different employed metrics to evaluate 
+the quality of the predictions. Finally, they present a table with many different works with the 
+identification of whether or not they employ the previously mentioned techniques. 
+One of the aspects of the present work is that, as happens with some of the examples given 
+above, it employs ontologies to organize and classify the items to be recommended in some way. 
+Two works can also be mentioned concerning tourism domain ontologies, but in this case their 
+formulation rather than their use. These works are by Ruíz-Martinez, J. et al. [65]  and Barta, R. 
+et al. [66] and they present different approaches to integrate and define tourism domain 
+ontologies. In the latter work an approach is presented that shows how to cover the semantic 
+space of tourism and be able to integrate different modularized ontologies. In the former, a 
+strategy to automatically instantiate and populate a domain ontology by extracting semantic 
+content from textual web documents. This work deals essentially with natural language 
+processing and named entity recognition, which are some of the techniques also employed in this 
+paper in terms of ontology population or, in other words, the classification of the different items to 
+recommend according to the ontology. 
+Many other works should also be referenced, this time not necessarily linked to the tourism theme, 
+but instead due to their focus on the algorithmic aspect or rather the recommendation strategy 
+regardless of its field of application. One particular type of recommender system that is very much 
+dominant in the literature in recent times is the context aware recommender system (CARS). The 
+work by Kulkarni, S. et al. [32] gives us a review on the state-of-the-art techniques employed in 
+
+4 
+ 
+context aware recommender systems. In this work the authors list the most common algorithmic 
+approaches from bio-inspired algorithms to other common and less common machine learning 
+algorithms and then enumerate the works that employed each type of solution. Another review 
+study on context aware recommender systems is authored by Haruna, K. et al. [67]. In this work, 
+the authors particularly emphasize the manner in which the contextual filtration is applied, for 
+which there are three variants, pre-filtering, post-filtering and context modelling. The difference 
+between each approach has to do with how context filtering is applied together with the process 
+of recommendation. Hence, in pre-filtering the recommender filters the items prior to 
+recommendation, while in post-filtering the opposite happens. In context modelling there is a more 
+complex integration of the context filtering and the recommendations. The authors then go on to 
+classify the different works in the literature according to this and other topics such as employed 
+algorithms, etc. A third overview paper on the topic of CARS is the work by Raza, S. et al. [44]. 
+In this work, the authors focus on the type of algorithms, the dimensionality reduction techniques, 
+user modelling techniques and finally the evaluation metrics and datasets employed. Still focusing 
+on CARS, a context-aware knowledge-based recommender system for movie showtimes called 
+RecomMetz is presented in the work by Colombo-Mendoza, L. et al. [58]. In this work, the CARS 
+developed has time awareness, crowd awareness and location awareness, as part of its context 
+awareness composition. It is interesting to verify that its location awareness employs an 
+exponential distance decay that discards items that are far away from the user. This sort of 
+mechanism is also employed in the current work but with other goals. A last example on CARS is 
+a genetic algorithm (GA) approach based on spatio-temporal aspects [68] by Linda, S. et al. Here, 
+the interesting aspect is the inclusion of a GA to optimize the temporal weights of each individual 
+while employing collaborative filtering for the recommendations. 
+Lately, one of the most studied techniques for recommender systems have been Factorization 
+Machines (FM) [69]. In the present work, a field-aware version of this technique is employed, also 
+known as an FFM. This technique is a kind of collaborative filtering method that gained some 
+notoriety for solving click-through prediction rates [64], among other problems. Several versions 
+exist of these FMs in the literature, with ensembles with deep neural networks [45], for example, 
+being one of such versions. The value of FM is that they are more powerful than traditional matrix 
+factorization techniques, being able to incorporate features and information such as implicit 
+feedback. For these reasons, an FM, more specifically an FFM, is one of the recommenders 
+employed in the proposed recommender system, constituting the collaborative filtering 
+component of the proposed RS.  
+ 
+ 
+ 
+
+5 
+ 
+1.2 
+Description of the RS and field of application 
+The proposed RS in this work is to be applied in the tourism industry. More specifically, the project 
+entails the creation of a recommender system to be used by hotel companies to recommend to 
+their guests their vast lists of partners in the region. It is very common that large hotel companies 
+have hundreds of partners offering products and most hotel guests are unaware of most of them. 
+The partners usually offer a wide array of products, which need an ontology to be organized and 
+better recommended. The proposed RS starts by having a Partner Management Platform (PMP) 
+for the hotel’s partners where they can manually introduce the items they want to be 
+recommended in the RS. The PMP, which is essentially an interface of the Item DB, feeds the 
+Domain Ontology which exists in a graph DB. The users are clients of the hotel that have checked-
+in, and they exist in the User DB, which houses not only demographic information but also user 
+preferences which are collected and inferred by the RS. The RS interface is a web-app which is 
+presented in a further section of the paper. In the following sections more detail is provided 
+concerning the various components of the RS, starting with the presentation of the RS 
+architecture in the following section.  
+ 
+2 
+Architecture and frameworks of the recommender system 
+The architecture of the RS can be essentially divided into 4 parts, the data repository, the context-
+aware subsystem, the recommender system per se and the user interface. In the following figure 
+the architecture is presented with each of its subcomponents. An overview of each of the 
+subcomponents is given in the following subsections. 
+ 
+Figure 1 Architecture of the RS. 
+ 
+2.1 
+Data repository 
+The first element of the recommender system is its data repository, in the sense that this is where 
+it starts, particularly with the Partner Management Platform (PMP). It is through this PMP that we 
+
+Location-aware
+Weather-aware
+Repetition-aware
+Userprofile
+manager
+Context-awareSubsystem
+Preference
+UserInterface
+manager
+ItemDB
+UserDB
+Domain
+Ontology
+Recommender
+pool
+Partner
+Management
+Recommender
+Platform
+Data Repository
+System6 
+ 
+have the introduction of the items, by the partners, to be recommended by the RS. In the PMP, 
+the partners introduce the items alongside necessary description and keywords. This information 
+introduced in the PMP is organized into an Item DB and later inserted into the domain ontology, 
+which is later explained in detail. 
+Other than the PMP with its Item DB and the mentioned domain ontology, the data repository also 
+has a User DB. This DB has both the demographic information collected from the users that 
+check-in to the hotel, but also the preference vectors that are inferred and managed by the RS. 
+The RS uses these two components of the user info to make predictions and to build different 
+recommendation models based on demographic, content, and collaborative filtering techniques. 
+ 
+2.1.1 Domain ontology - Neo4j and automatic population of ontology 
+As for the domain ontology, the initial approach was to adopt the ontology presented in SigTur 
+[8]. In addition, Neo4j (www.neo4j.com), which is a graph DB, was chosen to house the ontology 
+and to facilitate the automatic ontological extension with the items from the PMP. In the following 
+figures, the original ontology is shown already inserted in a Neo4j graph. 
+ 
+Figure 2 Ontology inserted in Neo4j. 
+
+Shopping
+Wine
+SCO
+Wine_E..
+Popular.
+SCO
+Music_F.
+NightLife
+Sco
+SCO
+SCo
+sCO
+BookF
+Gastron..
+Leisure
+SCO
+Leisure.
+SCO
+Oos
+SCo
+Gastron.
+SCO
+Events
+SCO
+Sco
+Health
+SCO
+Tradifion.
+Relaxafi..
+Gastron.
+Sport_ E.
+Sco
+TownR.
+Relaxafi..
+$Co
+Arts_An.
+Sco
+ScO
+Towns
+SCO
+Sco
+SCO
+SCC
+NonAqu.
+sCO
+Sport_R..
+SCO
+Air_Spor.
+SCo
+Culture
+SCo
+Tradition..
+Sco
+SCo -
+ SCO
+Sco
+Sports
+Culture
+SCO
+Tradition.
+Driving.
+MotorSp.
+Sco
+Aquatic_
+Nature
+Sco
+Climbing
+Sco
+Monume.
+SCO
+Ethnogr
+OOS
+Saiting
+Culture.
+SCo
+Surfing
+Nature
+UnderW.
+ViewPoi.
+8
+SCO
+Archeol.
+sco
+8
+$CO
+Protecte.
+Art_Mus.
+LandSc.
+Nature
+History.
+ichitect
+SCo
+SCO
+SCO
+Mountai.
+Coastal.
+Inland
+Rural_A.7 
+ 
+    
+ 
+Figure 3 Sample of the ontology (highlighted section in previous figure). 
+ 
+The advantage of using the Neo4j framework is that it facilitates the automation of ontological 
+extension. This ontological extension is achieved through the use of NLP techniques, such as 
+named entity recognition and cosine similarity between semantic concepts, using the spaCy 
+Python library integrated with Neo4j methods. These processes start with the insertion of the 
+items from the PMP or the Item DB. These items are parsed and tokenized, using both the item 
+descriptions and/or keywords. These parsed and tokenized items are then linked to the ontology 
+by means of semantic similarity between its keywords and description with each of the ontological 
+subclasses. The similarity scores above a given threshold originate a link between the item and 
+that specific ontological subclass. This process that ends with concept similarity and starts with 
+parsing, removal of stopwords and tokenization is performed with methods in the spaCy library. 
+The concept similarity is performed using spaCy’s vast pretrained word vectors. In addition, 
+named entity recognition is also performed on the items, automatically linking a Wikipedia entry, 
+if such entry exists. In Figure 4, a representation of the ontology after being extended with some 
+items, via the described process. One can see the original nodes in orange, that belong to the 
+ontology classes, some of which are now linked to grey nodes representing the items. The green 
+nodes represent the Wikipedia page object when such an object was found. In Figure 5 a zoomed 
+view of the highlighted zone in Figure 4 is shown. One can see two instances in which a Wikipedia 
+page object was found from the Named Entity Recognition procedure. The items were linked to 
+the ontology subclasses and one can observe that the links make sense in these cases, with 
+driving an F1 racecar linked to “Motor Sports”, and golf lessons and discounts on clubs linked to 
+“Golf”. 
+ 
+ ie  oi 
+ useums
+ istory  
+Culture  
+A uatic  
+ usic   
+Sailing
+ nder  
+Rural A 
+ onume 
+ ature
+Surfing
+ ight ife
+ ealth  
+ o ns
+ radition 
+ ood
+ eaches
+Culture
+Gastron 
+ radition 
+ ine   
+ ature  
+Air Spor 
+ ature  
+Golf
+ vents
+ otorSp 
+ oo    
+Culture  
+ riving  
+Shopping
+Gastron 
+ eisure  
+Relaxati 
+ eisure
+ ine
+Adventu 
+Climbing
+Arts An 
+ andSc 
+Relaxati 
+Gastron 
+Sport R 
+Sport   
+Architect 
+Routes
+Archeol 
+ radition 
+Art  us 
+Inland  
+Sports
+Coastal 
+ thnogr 
+ rotecte 
+ o n R 
+ ance  
+ onA u 
+ ountai 
+ opular 
+
+8 
+ 
+ 
+Figure 4 Ontology extended with the addition of items. 
+ 
+
+9 
+ 
+ 
+Figure 5 Sample of the extended ontology (highlighted section in previous figure). 
+ 
+The recommender system module then imports the extended ontology, both the classes and the 
+items. It will use the extended ontology to give content-based recommendations. 
+ 
+2.2 
+Context-aware subsystem module 
+The context-aware subsystem module does item pre-filtering on the basis of three context 
+submodules: location-aware, weather-aware and repetition-aware. In the case of the location-
+aware submodule, the objective is to filter out the hotel partners that are not located close by to a 
+specific instance of the hotel. Since the hotel company can have a wide array of partners that 
+may, in many cases, be close to one specific hotel but not to other hotels in other locations, such 
+as local or regional partners that only provide services to the hotels in the area, a first contextual 
+filtering phase is to apply location pre-filtering. Then we go on to the weather-aware submodule, 
+where the ontological sub-classes are associated with a given fuzzy definition of when they make 
+sense to be recommended, for example the beach ontology class or the outdoor sports ontology 
+class would tend to be penalized with bad weather. Finally, a third module, which is very much 
+novel, which is the repetition-aware module. Here, each ontological class would have a different 
+elapsed time parameter that affects an inverse exponential penalization factor to mimic the 
+repeatability of a given item. For example, one would probably be more adept to repeat a 
+restaurant than a museum in the same week. So, different ontological classes have different 
+factors that affect the inverse exponential function, that we may call the unwillingness to repeat 
+function, which defines how soon a user may be willing to repeat a given item. 
+ ie  oi 
+ useums
+ istory  
+Culture  
+A uatic  
+ usic   
+Sailing
+ nder  
+Rural A 
+ onume 
+ ature
+Surfing
+ ight ife
+ ealth  
+ o ns
+ radition 
+ ood
+ eaches
+Culture
+Gastron 
+ radition 
+ ine   
+ ature  
+A
+service
+that
+offers
+A
+tavern
+that
+serv 
+ ne
+of the
+main
+nigh 
+Surfing
+lessons
+Ancient
+history
+muse 
+Great
+meals
+that are
+tasty
+Rest
+and
+relaxa 
+visiting
+ isneyl 
+ atch a
+live
+football
+ edieval
+fair
+ atch a
+motogp
+race
+drive a
+  
+racecar
+ ry
+spearfis 
+ a e
+a trip in a
+hot air
+ball 
+Go
+shopping
+in our
+ne 
+ ry
+scubadi 
+ ne
+day
+snor  
+Golf
+lessons
+go to the
+spa
+ ry
+go  arts
+ ith your
+frien 
+Get a
+free pint
+at the
+pub
+ atch a
+Sporting
+C  m 
+ atch a
+S 
+ enfica
+ atch a
+ C  orto
+match
+Get a
+voucher
+for
+Sep 
+Get a
+free
+pi  a at
+ i  a
+ iscount
+for Call 
+ atch a
+live
+concert
+Get a
+discount
+for
+Co 
+Air Spor 
+ ature  
+Golf
+ vents
+ otorSp 
+ oo    
+Culture  
+ riving  
+Shopping
+Gastron 
+ eisure  
+Relaxati 
+ eisure
+ ine
+Adventu 
+Climbing
+Arts An 
+ andSc 
+Relaxati 
+Gastron 
+Sport R 
+Sport   
+Architect 
+Routes
+Archeol 
+ radition 
+Art  us 
+Inland  
+Sports
+Coastal 
+ thnogr 
+ rotecte 
+ o n R 
+ ance  
+ onA u 
+ ountai 
+ opular 
+
+10 
+ 
+ 
+2.3 
+Recommender system module 
+The recommender system module is the main module as the name entails. This module is 
+constituted by a user profile manager and a preference manager, besides the recommender pool. 
+Concerning the recommender pool and the models that compose it, that is addressed in depth in 
+Section 3 of this work. Here it suffices to say that the recommender pool is the set of different 
+recommender models that provide user recommendations. The models create an ensemble, 
+when more than one is active, that provides recommendations using different techniques and 
+approaches. 
+As for the remainder of the recommender system module, the user profile and the preference 
+manager, these two sub-modules manage the user related information, such as item ratings and 
+other user feedback in the case of the former, while the latter manages the user preference 
+vectors and propagates the user feedback on items to update the user preference vectors 
+accordingly. The way this is done will become clearer in the next sections. 
+ 
+2.4 
+User interface – web app 
+The last component is the user interface, which in this case is a web app that connects to the 
+recommender system module and other modules through a real-time and batch inference 
+endpoints that connect to ML pipelines defined in Azure. 
+
+11 
+ 
+ 
+Figure 6 App mockup showing the four main screens: welcome, preference definition, home and user profile. 
+ 
+In the previous figure one can observe the four different screens the user sees during his App 
+experience. The FILTER screen is only presented to the user on the first time he logs in and is, 
+in essence, a series of check boxes where the user defines his preferences. These check boxes 
+are used to give a first estimate on the user’s preferences concerning the ontology classes. The 
+user’s choices define his preference vectors which then are used to make content-based 
+recommendations. As for the HOME screen, it shows the different recommendations made to the 
+user by the RS, here the user can bookmark items, book items or mar  an item as “uninteresting”. 
+Finally, in the PROFILE screen, the user can observe his profile in terms preferences collected 
+and inferred by the RS as well as demographic information, such as date of birth, nationality, etc. 
+The different interactions the user can have with the App and the consequent interactions 
+between the App and the RS and back to the user are shown in Figure 7. In this figure one can 
+see how these interactions cascade and what the user gets back from each action he undertakes. 
+One can summarize the actions the user can take in the following:  
+• 
+Logging in  
+• 
+Preference input 
+• 
+Viewing recommendations 
+
+viser
+Adviser
+see
+syone
+syone
+YOU'RESTAYINGHERE
+Ldviser
+PAULAESTEVES
+Whatareyouinterested in?
+Hello
+HotelGoldenCrown
+MUSO
+Noture
+Paulo Esteves
+Vewpoinitsv
+HOTEL
+TMYPROFILE
+Concerte
+Le'sure
+Sports
+Walks
+Utorciaugue,faucibusatioculisid
+Nnrnec
+Pauio Esteves
+efficitursagittis diam.Etiom eget nunc
+RestourantsV
+Foutes
+Cinema
+DOB:
+10/03/1983
+acus
+Adcress: Ruo Efficitur:sogittis dion,#3,1c Lisboc
+Finess
+Beatchv
+Top:5
+Foryou
+Jeb:
+Sorior BIAnclyst
+PhasellusacportatellusVivamus
+EatProhik
+tempormattisultrces.Proinvitae
+Tellmemore
+conseouortortorguispnoretotortor
+A
+WHATWE'VELEARNEDABOUTYOU
+SKYDIVErush
+50%
+Ipere
+Foucbusoticcuisidetficit
+LEISURE
+ROUTES
+EVENTS
+FooFightersy
+tiverpoolFo
+22,
+gogittis Ciam.Etiam pgetnont
+locus.
+Francesinho
+Guzado
+START
+TOWNS
+CULTURE
+NATURE
+Dive classes
+VEWPOINTS
+SPORTS
+50%
+oucibuaticcuisi,eficitur
+2
+18.
+pogittisdigmEtiomegetmunt
+I'MALSOINTO:
+WELCOME
+Search fortopics you/reinterestedin
+Shortintroduction
+回
+T
+Woles
+Andeboly
+FILTER Screen
+HOME
+ACTMITES
+HISTORY
+MYPROTRE
+...
+Hke
+Guizodo
+Collectthefirstlayer
+ofinformationfrom
+HOMEScreen
+HONE
+ACTMTES
+ISTORY
+MYPRORLE
+the user
+Present the activities
+andpositions the user
+PROFILEScreen
+Consult andeditthe user's
+information12 
+ 
+• 
+Item feedback 
+• 
+Item booking 
+• 
+Item rating 
+ 
+ 
+Figure 7 User-App-RS interaction. User’s various possible actions and respective interactions between the 
+App and the RS. 
+ 
+3 
+Recommenders and stages in RS 
+The recommender system module mentioned in the previous section is composed by three 
+components: user profile manager, preference manager and recommender pool. The two former 
+ones have already been covered, and in this Section, the latter will be explained in depth. The 
+recommender pool is composed by four recommenders of different types: content-based, 
+popularity-based, demographic-based and collaborative. These four recommenders are modeled 
+with specific algorithms or employ specific techniques and they come into play in different phases 
+of maturity of the RS. These phases of maturity concern amount of data, that is, number of users 
+
+Yo
+RecSys
+User
+App
+1 User's first log in
+2 Asks preferences
+3 Inputspreferences
+4 Sendspreferences
+5Returnsrecommendations
+6Views recommendations
+7 Gives feedback and/or
+makesabooking
+-
+8Sendsfeedback
+9 Returns updated
+recommendations
+10Ratesbooked item
+11Sends itemrating
+(First rating in system)
+12Hybrid Recommender initiated
+13 Returns updated
+recommendations13 
+ 
+and rating density. Only after certain pre-specified values of users and rating density have been 
+reached are some of these methods activated, or in other words, are some of the phases reached. 
+In the following, the different phases and algorithms used are explained. 
+ 
+3.1 
+Phase 1 
+At the beginning, the RS is void of any ratings or users, and only items exist in the RS. When a 
+new user logs in for the first time, in order for the RS to make any meaningful recommendation, 
+some information has to be provided in the form of user preferences. This is, at this stage, the 
+only way to overcome cold-start issues.  he user’s preferences, which are associated to the 
+predetermined ontology are given and used to give content-based recommendations to the user. 
+The user then will provide explicit and implicit feedback, in the form of booking items, bookmarking 
+items or explicitly indicating they don’t li e the item. This feedback is then received by the RS who 
+then uses the said feedbac  to update the user’s preference vectors. This update originates new 
+recommendations to the user. 
+ 
+3.1.1 Preference vectors 
+At the core of phase 1 are the user preference vectors. These preference vectors are ontology 
+related and they are used to make content-based recommendations. There are three preference 
+vectors per user: 
+• 
+High-level preferences 
+• 
+Low-level preferences 
+• 
+Specific preferences 
+The high-level preferences are the ones the user identifies in the beginning and are associated 
+with the ontological super-classes. These classes are the most abstract classes and lower in 
+number. They are the first layer of ontological classes and are the ones that don’t have a parent 
+class and only child classes. Observing Figure 4, the Sports ontological class is an example of a 
+high-level preference since there is no ontology class above it. 
+The low-level preferences are associated to the ontological classes that link directly to the items. 
+These ontological classes are more specific, less abstract and in larger number. Observing Figure 
+4 and Figure 5, Golf is an example of a low-level preference, because two items link to it. 
+Finally, the specific preferences relate directly to the items, and is a vector that results from the 
+other two higher-level preference vectors and the user’s feedbac  on the items. 
+The way these vectors interact is explained in the following: 
+
+14 
+ 
+1. The user identifies the high-level preferences when he logs in for the first time. These 
+preferences are propagated by way of vector multiplication with the low-level ontological 
+preferences. 
+2. The low-level preferences are then propagated to the item level by way of vector 
+multiplication as well, originating the specific preference vector. The items are ranked, 
+and a subset of the highest ranked items are recommended to the user. 
+3. The user gives feedback on the recommendations by either bookmarking items, booking 
+items or dismissing items. The feedback is propagated upwards to the higher-level 
+preference vectors with different intensities. The low-level preference vector is strongly 
+affected, while the high-level preference vector is less affected because it is higher 
+upstream. This sort of “trickle-up” propagation of user feedback alters both high-level and 
+low-level preference vectors with different magnitude.  
+4. New item recommendations are calculated, this time using both the high-level and low-
+level preference vectors to predict whether an item should be recommended or not. The 
+prediction by each vector is weighed and aggregated originating an ensemble prediction 
+using both high and low preference vectors. The items are ranked, and a subset of the 
+highest ranked items are recommended to the user. 
+5. Repeat step 3. 
+ 
+3.1.2 Ontological content-based recommender 
+The content-based recommender is essentially vector multiplication between preference vectors 
+and content vectors. Content vectors are binary vectors which map one preference level to the 
+items content or to another preference vector content, while preference vectors show the intensity 
+levels of preference for each ontological category. 
+In step 4, the high and low preference vectors multiply with their corresponding item content vector 
+originating a content-based prediction. Both predictions are weighed and aggregated, and a 
+subset of the highest ran ed items is recommended to the user. After the user’s feedbac  both 
+preference vectors are updated according to the “tric le-up” propagation concept introduced 
+above. Then, new recommendations are calculated with the new preference vectors. 
+ 
+3.2 
+Phase 2 
+If the user booked and used an item, he can then rate said item, which will kickstart the hybrid 
+recommender composed by the initial content-based recommender and the new popularity-based 
+appendix. This popularity-based recommender uses a so-called damped mean on every item so 
+that little cardinality of ratings doesn’t give an exaggerated edge of an item over another, such as 
+an item with a single 5-star rating having a 5-star average.  
+
+15 
+ 
+𝐷𝑎𝑚𝑝𝑒𝑑 𝑀𝑒𝑎𝑛𝑗 = 
+∑
+𝑟𝑗𝑖 + 𝑘 ∙ 𝑟̿𝐺
+𝑛
+𝑖=1
+𝑛 + 𝑘
+ 
+Where 𝑟𝑗𝑖 is item j’s rating i, 𝑘 is the damping coefficient, 𝑟̿𝐺 is the global mean rating or some 
+other default value, and 𝑛 is the number of reviews of item j. 
+ 
+3.2.1 Hybrid recommender (content-based + popularity-based) 
+The start of the hybrid recommender marks the start of phase 2. At this point in the RS, there 
+aren’t many users and there aren’t many ratings.  he lac  in both mean that popularity-based, 
+demographic-based or collaborative approaches are still of little use. As more users join and more 
+ratings are given, other recommenders can become increasingly useful. As we reach a given 
+threshold of user and rating numbers we can initiate the demographic-based recommender. 
+The way in which the hybrid recommender uses both recommenders is by cascading ensemble. 
+That is, the popularity recommender pre-filters the items according to a rating threshold and then 
+the content-based recommender recommends items that were not eliminated by the popularity 
+recommender.  
+ 
+3.3 
+Phase 3 
+As more users are added to the RS, and as these users give feedback on recommended items, 
+other types of recommenders can enter the recommender pool. A first set of threshold values for 
+number of users and rating density is defined. When these thresholds are reached, phase 3 is 
+initiated with yet another recommender being added: the demographic-based recommender. 
+ 
+3.3.1 Demographic-based recommender 
+The demographic-based recommender is composed by two ML algorithms. One clustering 
+algorithm and one classification algorithm. The clustering algorithm has the purpose of identifying 
+clusters of similar users based on their demographic features.  he user’s demographic features 
+can be age, region/country, group composition, budget, academic degree, etc. These features 
+can be a mix of numerical, ordinal and nominal features and so a clustering algorithm that can 
+handle different data types is necessary. After the clustering has been performed, and the users 
+are all organized in clusters, a classification algorithm is used to predict whether a user will enjoy 
+each item based on the item feedback of other users in the same cluster. 
+For clustering, the algorithm employed was K-Prototypes, which works similarly to K-Means but 
+can deal with mixed data types, particularly ordinal and nominal data. To define the clustering 
+model, a knee region identifier is employed to automatically identify the optimal (or close to 
+
+16 
+ 
+optimal) number of clusters. The clustering model is retrained from time to time when sufficient 
+new users have been added since the last model fitting. 
+For classification a k-Nearest Neighbor algorithm, or kNN, was employed. Here, the users from 
+the same cluster are used to predict whether a given user will enjoy the items, based on those 
+users’ feedbac .  he     uses a custom distance metric that ta es into account both Jaccard 
+and Manhattan distance metrics for the ordinal and nominal features. The kNN than weighs the 
+opinion of the other users inversely proportional to their distance to the user to whom the 
+predictions are being made. The predictions given by this algorithm are weighed and added to 
+the predictions made by the hybrid recommender. 
+ 
+3.4 
+Phase 4 
+In phase 4, collaborative filtering is added to the pool. As it happens with phase 3, the entry into 
+phase 4 takes place when thresholds of user cardinality and rating density are reached. Once this 
+happens the collaborative filtering model is fitted and starts giving recommendations. The 
+algorithm used for collaborative filtering is a Field-Aware Factorization Machine (FFM), which has 
+already been introduced in Section 1. In the following sub-section, the FFM application is 
+explained in more detail. 
+ 
+3.4.1 Collaborative filtering with Field-Aware Factorization Machines (FFM) 
+To use FFMs, a specific Python library (xLearn) is used and the data also has to be transformed 
+into a specific format. A sample of a dataset in said format is shown in the following table. 
+ 
+Table 1 Dataset in the FFM format where each column represents a feature, except for column 0 which 
+represents the labels. 
+ 
+0 
+1 
+2 
+3 
+4 
+5 
+6 
+7 
+8 
+9 
+0 
+0 
+0:1:1 
+1:2:1 
+2:3:1 
+3:4:1 
+4:5:1 
+5:6:1 
+6:7:1 
+7:8:1 
+8:9:1 
+1 
+1 
+0:10:1 
+1:2:1 
+2:11:1 
+3:4:1 
+4:5:1 
+5:6:1 
+6:12:1 
+7:13:1 
+8:14:1 
+2 
+0 
+0:15:1 
+1:16:1 
+2:3:1 
+3:4:1 
+4:17:1 
+5:6:1 
+6:18:1 
+7:19:1 
+8:20:1 
+3 
+1 
+0:15:1 
+1:2:1 
+2:21:1 
+3:22:1 
+4:17:1 
+5:6:1 
+6:23:1 
+7:8:1 
+8:24:1 
+4 
+1 
+0:10:1 
+1:16:1 
+2:3:1 
+3:4:1 
+4:17:1 
+5:25:1 
+6:23:1 
+7:26:1 
+8:27:1 
+... 
+... 
+... 
+... 
+... 
+... 
+... 
+... 
+... 
+... 
+... 
+686422 
+1 
+0:1:1 
+1:2:1 
+2:3:1 
+3:4:1 
+4:17:1 
+5:25:1 
+6:23:1 
+7:8:1 
+8:37:1 
+686423 
+1 
+0:34:1 
+1:2:1 
+2:21:1 
+3:4:1 
+4:5:1 
+5:25:1 
+6:35:1 
+7:8:1 
+8:36:1 
+686424 
+1 
+0:10:1 
+1:16:1 
+2:3:1 
+3:4:1 
+4:17:1 
+5:25:1 
+6:18:1 
+7:8:1 
+8:24:1 
+686425 
+1 
+0:34:1 
+1:16:1 
+2:21:1 
+3:22:1 
+4:17:1 
+5:25:1 
+6:50:1 
+7:13:1 
+8:49:1 
+686426 
+1 
+0:15:1 
+1:2:1 
+2:3:1 
+3:4:1 
+4:17:1 
+5:6:1 
+6:23:1 
+7:8:1 
+8:44:1 
+ 
+
+17 
+ 
+This format is more complex than that for the Standard FM. This is due to the more complex 
+information that is ingested by the FFM which uses information about the fields to define the latent 
+vectors. That is, while in FMs each feature (field) has one latent vector, in FFMs this single 
+representation is broken down into multiple latent vectors, one to represent each other field. 
+𝑦̂(𝑥) ∶= 𝜔0 + ∑ 𝜔𝑖𝑥𝑖 + ∑ ∑ 〈𝕧𝑖, 𝕧𝑗〉𝑥𝑖𝑥𝑗
+𝑛
+𝑗=𝑖+1
+𝑛
+𝑖=1
+𝑛
+𝑖=1
+ 
+In the equation that represents the FM, which is shown above, the feature interactions 
+represented by 〈𝕧𝑖, 𝕧𝑗〉 would correspond to the following in our case scenario (user 
+demographic features): 
+𝑣𝑚𝑎𝑙𝑒 ∙ 𝑣𝑏𝑙𝑢𝑒𝑐𝑜𝑙𝑙𝑎𝑟 + 𝑣𝑚𝑎𝑙𝑒 ∙ 𝑣𝑙𝑜𝑤𝑏𝑢𝑑𝑔𝑒𝑡 + 𝑣𝑚𝑎𝑙𝑒 ∙ 𝑣𝑛𝑜𝑟𝑡ℎ𝑒𝑢𝑟𝑜𝑝𝑒 + ⋯ 
+That is, the male latent vector that multiplies with each other latent vector is the same. The idea 
+behind FFM is that the weight of the male latent vector might not be the same when multiplying 
+with the job latent vectors as they are with the budget latent vectors, and so on. Thus, in the FFM, 
+the latent vectors are field-aware, which results in the following: 
+𝑣𝑚𝑎𝑙𝑒,𝑗𝑜𝑏 ∙ 𝑣𝑏𝑙𝑢𝑒𝑐𝑜𝑙𝑙𝑎𝑟,𝑔𝑒𝑛𝑑𝑒𝑟 + 𝑣𝑚𝑎𝑙𝑒,𝑏𝑢𝑑𝑔𝑒𝑡 ∙ 𝑣𝑙𝑜𝑤𝑏𝑢𝑑𝑔𝑒𝑡,𝑔𝑒𝑛𝑑𝑒𝑟 + 𝑣𝑚𝑎𝑙𝑒,𝑟𝑒𝑔𝑖𝑜𝑛 ∙ 𝑣𝑛𝑜𝑟𝑡ℎ𝑒𝑢𝑟𝑜𝑝𝑒,𝑔𝑒𝑛𝑑𝑒𝑟 + ⋯ 
+ 
+Besides demographic features, as is shown in this example, the latent-vectors can also easily 
+incorporate item features as well as contextual features and can thus integrate context-awareness 
+in a deeper sense than simple contextual pre-filtering or post-filtering. 
+The FFM model represents the last phase addition to the recommender pool. The predictions 
+attained from it are weighed and then aggregated with the predictions given by the other two, the 
+hybrid and the demographic recommender. The weighs given to each recommender may be set 
+to change over time so that it accompanies the maturity and complexity of each of the 
+recommenders in the pool, thus giving progressively larger weight to the FFM as more users and 
+more ratings are added to the system. 
+
+18 
+ 
+ 
+Figure 8 Diagram of the various RS phases and interactions between RS and Data Repository (DB) 
+components.  
+
+V1.0
+4
+Phase1
+11
+Phase2
+Phase3
+5
+Phase4
+8&9
+Newuserlogsn
+Feedback
+Seneretes reApp
+Gets user from UserDB
+receivedfromAp
+toApp
+12
+Hybridt Rec ir
+Updates ontology
+Step4.5.8.9811repealedh
+AftermanyStep
+A4.5.8.9&11
+AnerSlep4
+589811
+GeneratestreAs
+Serenerates recs
+Phase3beqins.
+all threemodeis.
+Shokds for FFM reiraining
+en
+Rec initiated
+Recalculate clusters
+Demog ec cotnue
+Recaculalecstrs
+Clusters defined
+Collab
+FFMiniliated
+RetrainFFM.
+Sends ue lo ecomnender
+Ses ies to GraoDB.
+GraphDB
+Sennsertsilemontology
+SsnsertsnewiteminOntoloy19 
+ 
+4 
+Recommender system - Case study (CS) with synthetic data 
+One of the main challenges in designing the recommender system proposed in this work was the 
+lack of data to perform any type of experiment or even just to aid and inspire in the definition of 
+the algorithms to employ. The lack of data was absolute, both on the side of the items as on the 
+side of the users and preferences. The main issue is the non-existence of a dataset with user 
+demographic features and user preferences, since such a dataset would allow to overcome some 
+of the cold-start issues as well as give some idea of the data schema to be adopted. 
+As a result, and since no public datasets were found that could overcome this hinderance, the 
+decision was made to generate a synthetic dataset. The generated dataset was done so by using 
+many different techniques from gaussian copulas to fuzzy logic. Further information on that work 
+will be available in another paper by the author Camacho, VT. In the following sub-section, the 
+synthetic data employed in this  or ’s case study is presented. 
+Besides the synthetic data, a set of metrics was chosen to get an idea about the quality of the 
+results from the recommenders. Traditional ML metrics are not always adequate for RS, mainly 
+because, by principle, the objective of an RS is not to emulate exactly the choices of a given user 
+since, if that were the case, there  ouldn’t be a need for an RS in the first place. In the metrics 
+sub-section, the set of used metrics is presented. 
+The remainder of this section is applying the recommenders introduced in the previous section 
+and testing them with different amounts of data which will attempt to emulate the data present at 
+the different phases. 
+ 
+4.1 
+Synthetic data 
+In the work mentioned above, a methodology for the generation of synthetic datasets for 
+recommender systems is presented, thus allowing to overcome the obstacle of not having quality 
+data in sufficient amount (or even at all) readily available. The difficulties that are associated with 
+this task are essentially the definition of a dataset with multiple datatypes, such as numerical 
+(continuous), ordinal and nominal, and with different levels of correlation among the data, as well 
+as the definition of user-ratings based on well-defined latent user preferences. To overcome this, 
+a methodology was devised where several different techniques are employed in sequence to 
+create the datasets concerning user characteristics, item properties, item categories and latent 
+user preferences associated to user and item features, and as a result, a user-item sparse ratings 
+matrix. The output of the methodology is: 
+1) Item dataset with item names and categories. 
+2) User dataset with user characteristics (demographic features). 
+3) User-item sparse ratings matrix. 
+
+20 
+ 
+4) Latent preferences and Multinomial Logit model to compare with the outputs of the 
+Recommender System. 
+ 
+4.1.1 Data Schema 
+From the output presented above, we can see 4 DataFrames with different information. These 
+DataFrames each have their own schema and have features from different data types. In the 
+following, the created DataFrames are introduced: 
+• 
+Demographic Features 
+• 
+Preferences 
+• 
+Item Features 
+• 
+User Ratings 
+Going into more detail regarding the user demographic features DataFrame: 
+• 
+Demographic Features: 
+o 
+User ID 
+o 
+Age 
+o 
+Gender 
+o 
+Job 
+o 
+Academic Degree 
+o 
+Budget 
+o 
+Country/Region 
+o 
+Group Composition 
+o 
+Accommodation 
+Concerning the type of feature, they can be divided essentially into three groups: numerical, 
+categorical ordinal and categorical nominal. Concerning numerical and categorical ordinal 
+features, we have the following: 
+• 
+Numerical 
+o 
+Age – numerical (can be transformed into age bins) 
+• 
+Ordinal: 
+o 
+Age bins = ['18-30','31-40', '41-50', '51-60', '60+'] 
+o 
+Academic Degree = ['None', 'High School', 'Some College', 'College Degree'] 
+o 
+Budget = ['Low', 'Mid', 'High'] 
+o 
+Accommodation = ['Single', 'Double', 'Suite', 'Villa'] 
+As for categorical nominal features, the following were modelled: 
+• 
+Gender = ['Male', 'Female'] 
+• 
+Job = ['Blue Collar', 'White Collar'] 
+
+21 
+ 
+• 
+Country/Region = ['South Europe', 'North Europe', 'East Europe', 'North America', 'South 
+America', 'Asia', 'Africa', 'Middle East'] 
+• 
+Group Composition = ['1 Adult', '2 Adults', '2 Adults + Child', 'Group of Friends'] 
+ 
+4.1.2 Samples of the generated DataFrames 
+The resulting DataFrames (DF) can be used to train and test RS. In the case of the present work, 
+they are used to simulate the different phases of data availability, thus testing the recommenders 
+employed in each of the four phases. In the following, samples of the generated DFs are 
+presented. The first sample shown is the User DF in Table 2. This DF is composed by the user 
+demographic features and UserID. The demographic features are ordinal (Age, AcDeg, Budget, 
+Accom) and nominal (Gender, Job, Region, GroupComp). The entire set of users created has 
+cardinality of 100,000. 
+ 
+Table 2 User DF composed by the demographic features of the users. 
+UserID 
+Age 
+AcDeg 
+Budget 
+Accom 
+Gender 
+Job 
+Region 
+GroupComp 
+0 
+4 
+2 
+1 
+2 
+Female 
+blue collar 
+North Europe 
+2Adlt 
+1 
+5 
+4 
+2 
+3 
+Male 
+white collar 
+North Europe 
+GrpFriends 
+2 
+3 
+3 
+2 
+2 
+Female 
+blue collar 
+North Europe 
+2Adlt+Child 
+3 
+4 
+4 
+2 
+2 
+Female 
+white collar 
+North Europe 
+2Adlt+Child 
+4 
+3 
+3 
+2 
+3 
+Female 
+white collar 
+South Europe 
+2Adlt 
+... 
+... 
+... 
+... 
+... 
+... 
+... 
+... 
+... 
+99995 
+4 
+4 
+2 
+2 
+Female 
+white collar 
+North Europe 
+2Adlt+Child 
+99996 
+3 
+4 
+3 
+2 
+Male 
+white collar 
+Asia 
+2Adlt+Child 
+99997 
+1 
+1 
+1 
+1 
+Female 
+blue collar 
+South Europe 
+2Adlt 
+99998 
+1 
+3 
+1 
+2 
+Female 
+blue collar 
+South Europe 
+2Adlt+Child 
+99999 
+4 
+3 
+2 
+2 
+Male 
+blue collar 
+North America 
+2Adlt+Child 
+ 
+The second DF is the User-Preference DF which contains the latent preferences and is presented 
+in Table 3. These latent preferences are related to the ontology classes. The latent preferences 
+of each user were modeled through a multinomial logit model based on their demographic 
+features. This DF shows the relative interest of a given user in a given preference category versus 
+any other preference category. The values between different users are not comparable. 
+ 
+Table 3 User-Preference DF containing the latent preferences from the Multinomial Logit model. 
+UserID 
+Beach 
+Relax 
+Shop 
+Nightlife 
+Theme park 
+Gastro 
+Sports 
+Culture 
+Nature 
+Events 
+
+22 
+ 
+0 
+0 .408 
+0 .026 
+0 .020 
+0 .041 
+0 .002 
+0 .002 
+0 .004 
+0 .009 
+0 .487 
+0 .002 
+1 
+0 .002 
+0 .077 
+0 .017 
+0 .015 
+0 .009 
+0 .457 
+0 .041 
+0 .271 
+0 .107 
+0 .002 
+2 
+0 .554 
+0 .156 
+0 .039 
+0 .041 
+0 .027 
+0 .010 
+0 .021 
+0 .015 
+0 .135 
+0 .003 
+3 
+0 .005 
+0 .038 
+0 .012 
+0 .000 
+0 .003 
+0 .252 
+0 .003 
+0 .674 
+0 .009 
+0 .002 
+4 
+0 .002 
+0 .229 
+0 .003 
+0 .001 
+0 .000 
+0 .137 
+0 .001 
+0 .623 
+0 .000 
+0 .002 
+... 
+. . . 
+. . . 
+. . . 
+. . . 
+. . . 
+. . . 
+. . . 
+. . . 
+. . . 
+. . . 
+99995 
+0 .003 
+0 .106 
+0 .202 
+0 .000 
+0 .020 
+0 .115 
+0 .005 
+0 .202 
+0 .337 
+0 .010 
+99996 
+0 .001 
+0 .127 
+0 .064 
+0 .000 
+0 .002 
+0 .034 
+0 .001 
+0 .750 
+0 .016 
+0 .005 
+99997 
+0 .050 
+0 .285 
+0 .030 
+0 .337 
+0 .110 
+0 .006 
+0 .091 
+0 .019 
+0 .015 
+0 .057 
+99998 
+0 .031 
+0 .712 
+0 .007 
+0 .083 
+0 .103 
+0 .004 
+0 .021 
+0 .027 
+0 .006 
+0 .007 
+99999 
+0 .005 
+0 .880 
+0 .064 
+0 .000 
+0 .035 
+0 .000 
+0 .009 
+0 .003 
+0 .002 
+0 .003 
+ 
+The third DF sample presented is the Item DF in Table 4. Here a set of 29 items were included 
+belonging to different categories which are the user latent preferences presented in the previous 
+table.  
+ 
+Table 4 Item DF with corresponding item category (ontology and latent preferences). 
+itemID 
+Item Name 
+Category 
+0 
+A service that offers you the opportunity to 
+do bungee-jumping 
+['Leisure', 'Sports', 'Routes', 'Events', 
+'Nature'] 
+1 
+A tavern that serves traditional food 
+['Leisure', 'Events', 'Culture', 'Towns'] 
+2 
+Ancient history museum 
+['Culture', 'ViewPoints', 'Events', 
+'Nature', 'Routes', 'Towns'] 
+3 
+Discount for Callaway clubs 
+['Sports'] 
+4 
+Get a discount for Comic-Con 
+['Sports'] 
+5 
+Get a free pint at the pub 
+['Events', 'Leisure'] 
+6 
+Get a free pizza at Pizza Hut 
+['Leisure'] 
+7 
+Get a voucher for Sephora 
+['Leisure'] 
+8 
+Go shopping in our new mall 
+['Leisure'] 
+9 
+Golf lessons 
+['Sports', 'Leisure', 'Events'] 
+
+23 
+ 
+10 
+Great meals that are tasty 
+['Leisure', 'Events'] 
+11 
+Medieval fair 
+['Culture', 'Events', 'Nature', 'Towns'] 
+12 
+One day snorkeling with the fish 
+['Sports', 'Leisure', 'Nature'] 
+13 
+One of the main nightclubs in the city 
+['Culture', 'Events', 'Nature', 'Leisure', 
+'Routes', 'Towns'] 
+14 
+Rest and relaxation at the spa 
+['Leisure', 'Routes'] 
+15 
+Surfing lessons 
+['Sports'] 
+16 
+Take a trip in a hot-air balloon 
+['Sports'] 
+17 
+Try go-karts with your friends 
+['Sports'] 
+18 
+Try scubadiving 
+['Sports'] 
+19 
+Try spearfishing with a pro 
+['Sports'] 
+20 
+Watch a FC Porto match 
+['Events', 'Sports'] 
+21 
+Watch a SL Benfica match 
+['Events', 'Sports'] 
+22 
+Watch a Sporting CP match 
+['Sports', 'Events'] 
+23 
+Watch a live concert of Mastodon 
+['Events'] 
+24 
+Watch a live football match 
+['Sports', 'Events'] 
+25 
+Watch a motogp race 
+['Events', 'Sports'] 
+26 
+drive a F1 racecar 
+['Sports'] 
+27 
+go to the spa 
+['Leisure'] 
+28 
+visiting Disneyland 
+['Leisure'] 
+ 
+The last data sample is the result of an external product between the user preferences from the 
+multinomial logit model and the item DF. The result is the input of a Fuzzy Inference System, 
+which along with other implicit information on user and items returns the User-Item ratings DF, a 
+sample of which is shown in Table 5.  
+ 
+Table 5 User-Item ratings DF. 
+ 
+0 
+1 
+2 
+3 
+4 
+5 
+… 
+23 
+24 
+25 
+26 
+27 
+28 
+ 
+userId 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+0 
+1.41 
+0.00 
+1.87 
+0.00 
+3.21 
+0.00 
+… 
+0.00 
+1.79 
+0.00 
+1.79 
+2.96 
+0.00 
+ 
+1 
+0.00 
+4.63 
+1.77 
+1.26 
+0.00 
+0.00 
+… 
+0.00 
+0.00 
+4.06 
+0.00 
+2.21 
+1.77 
+2 
+0.00 
+0.00 
+0.00 
+2.10 
+3.20 
+2.38 
+… 
+3.48 
+0.00 
+0.00 
+0.00 
+0.00 
+0.00 
+ 
+3 
+0.00 
+3.12 
+0.00 
+0.00 
+3.28 
+2.89 
+… 
+0.00 
+2.22 
+0.00 
+0.00 
+0.00 
+0.00 
+ 
+4 
+1.37 
+0.00 
+2.31 
+1.63 
+0.00 
+0.00 
+… 
+3.31 
+2.30 
+0.00 
+0.00 
+0.00 
+0.00 
+ 
+… 
+… 
+… 
+… 
+… 
+… 
+… 
+… 
+ 
+… 
+… 
+… 
+… 
+… 
+… 
+99995 
+0.00 
+0.00 
+0.00 
+1.21 
+3.42 
+0.00 
+… 
+0.00 
+3.84 
+3.79 
+0.00 
+3.36 
+0.00 
+ 
+99996 
+1.46 
+0.00 
+0.00 
+0.00 
+2.31 
+0.00 
+… 
+2.31 
+0.00 
+0.00 
+0.00 
+0.00 
+1.39 
+99997 
+1.47 
+0.00 
+0.00 
+1.32 
+2.74 
+0.00 
+…. 
+0.00 
+0.00 
+2.29 
+0.00 
+0.00 
+0.00 
+ 
+99998 
+0.00 
+4.64 
+4.11 
+1.78 
+0.00 
+2.94 
+… 
+3.43 
+2.65 
+3.80 
+0.00 
+4.65 
+4.33 
+99999 
+0.00 
+3.54 
+3.06 
+0.00 
+4.07 
+2.65 
+… 
+0.00 
+3.07 
+3.51 
+2.46 
+3.50 
+2.61 
+ 
+
+24 
+ 
+ 
+ 
+4.2 
+Metrics 
+The metrics for a RS are not a trivial issue. Many works tend to use common ML metrics, such 
+as classification metrics like precision, recall, accuracy, or regression metrics such as RMSE or 
+MAE when the goal is to perform a regression on 1-5 ratings, for example. However, these metrics 
+imply that the data available to us about user behavior is perfect, that is, users are aware of all 
+the items they li e and the ones they haven’t tried aren’t as relevant. If this were the case, no RS 
+would be needed in the first place. The drawback of using this type of metrics is that it can 
+encourage the recommender to make obvious recommendations in some cases, by penalizing 
+wrong recommendations too much. In addition, these metrics do nothing to the tune of comparing 
+recommenders based on how personalized its recommendations are, or how diversified. 
+Other metrics have been developed for RS in recent years that try to address these issues, some 
+of which are presented in the following. 
+ 
+1. Mean Average Precision @ K and Mean Average Recall @ K 
+As in more traditional machine learning, the dataset is split into training and test sets, and 
+the test set is comprised of cases the learner did not train on and thus it is used to 
+measure the model’s ability to generali e  ith ne  data. In recommender systems, the 
+same is done, and the output of a recommender system is usually a list of K 
+recommendations for each user in the test set, and to produce those recommendations 
+the recommender only trained on the items that user enjoyed in the training set. MAP@K 
+(Mean Average Precision @ K) gives insight to how relevant the list of recommended 
+items are, whereas MAR@K (Mean Average Recall @ K) gives insight to how well the 
+recommender system is able to discover all the items the user has rated positively in the 
+test set. 
+In recommender systems, precision and recall are essentially the same as in machine 
+learning: 
+𝑃𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛 = # 𝑜𝑓 𝑟𝑒𝑙𝑒𝑣𝑎𝑛𝑡 𝑟𝑒𝑐𝑜𝑚𝑚𝑒𝑛𝑑𝑎𝑡𝑖𝑜𝑛𝑠
+# 𝑜𝑓 𝑖𝑡𝑒𝑚𝑠 𝑟𝑒𝑐𝑜𝑚𝑚𝑒𝑛𝑑𝑒𝑑
+ 
+𝑅𝑒𝑐𝑎𝑙𝑙 = # 𝑜𝑓 𝑟𝑒𝑙𝑒𝑣𝑎𝑛𝑡 𝑟𝑒𝑐𝑜𝑚𝑚𝑒𝑛𝑑𝑎𝑡𝑖𝑜𝑛𝑠
+# 𝑜𝑓 𝑟𝑒𝑙𝑒𝑣𝑎𝑛𝑡 𝑖𝑡𝑒𝑚𝑠
+ 
+ o ever, these metrics don’t ta e ordering into account, and since the output of a 
+recommender system is usually an ordered list, the metrics at cut-off k are introduced, 
+MAP@K and MAR@K. 
+
+25 
+ 
+𝑀𝐴𝑃@𝐾 = 1
+|𝑈| ∑
+1
+min (𝑚, 𝐾)
+|𝑈|
+𝑢=1
+∑ 𝑃𝑢(𝑘) ∙ 𝑟𝑒𝑙𝑢(𝑘)
+𝐾
+𝑘=1
+ 
+𝑀𝐴𝑅@𝐾 = 1
+|𝑈| ∑ 1
+𝑚
+|𝑈|
+𝑢=1
+∑ 𝑟𝑢(𝑘) ∙ 𝑟𝑒𝑙𝑢(𝑘)
+𝐾
+𝑘=1
+ 
+Where 𝑈 is the set of users in the test set, 𝑚 is the number of relevant items for user 𝑢, 
+𝑃𝑢(𝑘) and 𝑟𝑢(𝑘), are the precision@k and recall@k, respectively, and 𝑟𝑒𝑙𝑢(𝑘) is a factor 
+equal to 1 if the 𝑘 th item is relevant, and 0 otherwise. 
+ 
+ 
+2. Coverage 
+ 
+Coverage is the percentage of items on the training data that the recommender is able to 
+recommend on a test set. 
+ 
+𝐶𝑜𝑣𝑒𝑟𝑎𝑔𝑒 = 𝐼
+𝑁 ∗ 100% 
+ 
+Where 𝐼 is the number of unique items the model recommends in the test data and 𝑁 is 
+the total number of unique items in the training data. 
+ 
+ 
+ 
+3. Personalization 
+Personalization is the dissimilarity between users lists of recommendations. A high score 
+indicates user lists are different between each other, while a low score indicates they are 
+very similar. Similarity between recommendation lists is calculated via the cosine 
+similarity between said lists and then by calculating the average of the upper triangle of 
+the cosine similarity matrix (avgCosim). The personalization is then given by: 
+𝑃𝑒𝑟𝑠𝑜𝑛𝑎𝑙𝑖𝑧𝑎𝑡𝑖𝑜𝑛 = 1 − 𝑎𝑣𝑔𝐶𝑜𝑠𝑖𝑚 
+ 
+4. Diversity  
+Diversity measures how different are the items being recommended to the user. 
+𝐷𝑖𝑣𝑒𝑟𝑠𝑖𝑡𝑦 = 1 − 𝑖𝑙𝑠 
+
+26 
+ 
+Where 𝑖𝑙𝑠 corresponds to intra-list similarity, which is the average cosine similarity of all 
+items in a list of recommendations. This calculation uses features of the recommended 
+items (such as item metadata) to calculate the similarity. The feature matrix is indexed by 
+the item id and includes one-hot-encoded features. If a recommender system is 
+recommending lists of very similar items, the intra-list similarity will be high and 
+conversely, the diversity will be low. 
+ 
+5. Novelty 
+Finally, novelty measures the capacity of recommender systems to propose novel and 
+unexpected items which a user is unlikely to know about already. It uses the self-
+information of the recommended item, and it calculates the mean self-information per top-
+N recommended list and averages them over all users. 
+𝑁𝑜𝑣𝑒𝑙𝑡𝑦 = 1
+|𝑈| ∑ ∑
+𝑙𝑜𝑔2 (𝑐𝑜𝑢𝑛𝑡(𝑖)
+|𝑈|
+)
+|𝑁|
+|𝑁|
+𝑖=1
+|𝑈|
+𝑢=1
+ 
+Where 𝑈 is the user list, 𝑁 is the top n-list and 𝑐𝑜𝑢𝑛𝑡(𝑖) is the number of users that have 
+consumed the specific item. 
+ 
+4.3 
+CS with increasing data quantity 
+In this sub-section the previously presented datasets and the previously presented metrics are 
+employed to test and evaluate the RS in its various phases. For this to work, the datasets will be 
+gradually incremented, starting with very few users and no ratings, and ending with the full 
+datasets. This process is meant to mimic the natural evolution of a RS, from initial cold-start 
+conditions to thousands of users with thousands of reviews. In each phase different 
+recommenders are employed as was already mentioned in previous sections. 
+ 
+4.3.1 CS in Phase 1 
+As mentioned previously, phase 1 is characterized by little number of users and no ratings. At this 
+point, only content-based approaches are possible, and only if there is some input from the user 
+concerning his preferences, which the RS asks when the user first logs in. Otherwise, the RS 
+would be incapable of giving any recommendation short of a random context-filtered one. To 
+mimic this first stage, 98 initial users are added to the RS. Each user inputs their HL preference 
+vector related to Table 3, which the phase 1 content-based recommender uses to generate 
+recommendations. Unlike in Table 3, the HL preference vector takes either 0 or 1 values and thus 
+not conveying information on interest intensity. In the following tables, a sample of the 98 users 
+and their respective HL vectors are shown. 
+
+27 
+ 
+Table 6 High-level preferences of the users. 
+userId 
+ViewPoints 
+Nature 
+Towns 
+Culture 
+Events 
+Leisure 
+Routes 
+Sports 
+1 
+0 
+0 
+0 
+0 
+0 
+1 
+0 
+0 
+2 
+1 
+0 
+1 
+0 
+0 
+1 
+1 
+0 
+3 
+0 
+0 
+0 
+0 
+0 
+1 
+0 
+0 
+4 
+0 
+0 
+0 
+0 
+0 
+1 
+1 
+1 
+5 
+0 
+0 
+1 
+0 
+0 
+0 
+0 
+0 
+… 
+… 
+… 
+… 
+… 
+… 
+… 
+… 
+… 
+94 
+0 
+0 
+0 
+0 
+0 
+1 
+0 
+0 
+95 
+0 
+0 
+0 
+0 
+0 
+1 
+0 
+0 
+96 
+1 
+0 
+1 
+0 
+0 
+1 
+1 
+0 
+97 
+0 
+0 
+1 
+0 
+0 
+0 
+0 
+0 
+98 
+1 
+0 
+1 
+1 
+0 
+0 
+1 
+0 
+ 
+The recommendations given by the RS for each user are in the following table. We can apply all 
+previously presented metrics to these results, including MAP@K and MAR@K because we are 
+aware of some ratings given by the users, present in the User-Item ratings DF which we can use 
+for this purpose. 
+ 
+Table 7 Sample of the recommendations given to the users by the content recommender. 
+userId 
+Recommendations 
+1 
+[(6, 'Get a free pizza at Pizza Hut'), (7, 'Get a voucher for Sephora'), (8, 'Go 
+shopping in our new mall'), (27, 'go to the spa'), (28, 'visiting Disneyland')] 
+2 
+[(6, 'Get a free pizza at Pizza Hut'), (7, 'Get a voucher for Sephora'), (8, 'Go 
+shopping in our new mall'), (14, 'Rest and relaxation at the spa'), (27, 'go to the 
+spa')] 
+3 
+[(6, 'Get a free pizza at Pizza Hut'), (7, 'Get a voucher for Sephora'), (8, 'Go 
+shopping in our new mall'), (27, 'go to the spa'), (28, 'visiting Disneyland')] 
+4 
+[(4, 'Get a discount for Comic-Con'), (6, 'Get a free pizza at Pizza Hut'), (7, 'Get a 
+voucher for Sephora'), (8, 'Go shopping in our new mall'), (14, 'Rest and relaxation 
+at the spa')] 
+5 
+[(11, 'Medieval fair'), (1, 'A tavern that serves traditional food'), (13, 'One of the 
+main nightclubs in the city'), (2, 'Ancient history museum'), (0, 'A service that offers 
+you the opportunity to do bungee-jumping')] 
+… 
+… 
+94 
+[(6, 'Get a free pizza at Pizza Hut'), (7, 'Get a voucher for Sephora'), (8, 'Go 
+shopping in our new mall'), (27, 'go to the spa'), (28, 'visiting Disneyland')] 
+
+28 
+ 
+95 
+[(6, 'Get a free pizza at Pizza Hut'), (7, 'Get a voucher for Sephora'), (8, 'Go 
+shopping in our new mall'), (27, 'go to the spa'), (28, 'visiting Disneyland')] 
+96 
+[(6, 'Get a free pizza at Pizza Hut'), (7, 'Get a voucher for Sephora'), (8, 'Go 
+shopping in our new mall'), (14, 'Rest and relaxation at the spa'), (27, 'go to the 
+spa')] 
+97 
+[(11, 'Medieval fair'), (1, 'A tavern that serves traditional food'), (13, 'One of the 
+main nightclubs in the city'), (2, 'Ancient history museum'), (0, 'A service that offers 
+you the opportunity to do bungee-jumping')] 
+98 
+[(2, 'Ancient history museum'), (11, 'Medieval fair'), (13, 'One of the main 
+nightclubs in the city'), (1, 'A tavern that serves traditional food'), (14, 'Rest and 
+relaxation at the spa')] 
+ 
+ 
+Table 8 Values for the various metrics on the content model recommendations. 
+MAP@K 
+MAR@K 
+Coverage 
+Personalization 
+Diversity HL 
+Diversity LL 
+Novelty 
+0.092 
+0.092 
+0.55 
+0.51 
+0.21 
+0.76 
+0.66 
+ 
+We can see that mean average precision and mean average recall have the same value, the 
+value at K is equal to 5, since the recommender recommends 5 items to each user. The two 
+diversity values pertain to high level and low-level preferences showing how diverse are the 
+recommendations in terms of recommending diverse items. It is expected for the high-level 
+diversity to be lower than the low-level diversity since the content recommender makes 
+recommendations based on high-level preferences of the users. Low-level preferences are linked 
+ontologically to high-level preferences, but they are greater in variety, hence the same higl-level 
+preference is linked to many low-level preferences, this justifies the larger value of Diversity LL 
+compared to Diversity HL. Coverage, personalization and both diversities return values from 0 to 
+1, where 1 represents maximum coverage, personalization and diversity. The value for novelty 
+can take any positive value, the greater the value the more unexpected recommendations are 
+given based on popularity. In this study, the metric for novelty may not be very useful due to the 
+relatively low cardinality of items and the fact that there are no less popular items per se, at least 
+not very noticeably. In any case, these metrics are more useful in when used to compare different 
+models. 
+ 
+ 
+ 
+ 
+
+29 
+ 
+4.3.2 CS in Phase 2 
+In phase 2 there are ratings in the system, although not enough users to feed the demographic-
+based recommender. In this phase we can simulate an RS state where there are 98 users and 
+64 ratings. The hybrid recommender is a hybridization of the initial content-based recommender 
+with the new popularity-based recommender. The ratings are used to filter out items with average 
+rating below a given threshold. Once again, the same metrics are applied, and the results are 
+shown in the following table. 
+ 
+Table 9 Values for the various metrics on the hybrid model recommendations. 
+MAP@K 
+MAR@K 
+Coverage 
+Personalization 
+Diversity HL 
+Diversity LL 
+Novelty 
+0.219 
+0.219 
+0.17 
+1.11e-16 
+0.64 
+0.91 
+0.66 
+ 
+It is interesting to observe that the precision and recall have gone up, which makes sense because 
+the items are now being filtered according to rating and higher rating items are more prone to 
+having been liked by the users, at least the synthetic data was defined as such. The coverage 
+has gone down, which makes sense since less items are being recommended due to filtering. 
+Personalization has gone down since it now many users are being recommended the same items. 
+Diversity has gone up; this can be due to recommending some items outside of the natural 
+preference of the user due to ratings filtering. All in all, differences can be observed compared to 
+the content-recommender, these differences make sense and seem to go towards an expected 
+behavior by the recommender. 
+ 
+4.3.3 CS in Phase 3 
+In phase 3, enough users with ratings given have been introduced in the system to kickstart the 
+demographic-based recommender. This recommender works by defining user clusters based on 
+demographic features and then giving item recommendations based on the predictions of a kNN. 
+This phase 3 recommender works together with the hybrid recommender from phase 2. In the 
+following table, the metrics are applied, and the results shown. The number of users in this phase 
+total 198, with 191 ratings. 
+ 
+Table 10 Values for the various metrics on the hybrid and demographic model recommendations. 
+ 
+MAP@K MAR@K 
+Coverage 
+Personalization 
+Diversity HL 
+Diversity LL 
+Novelty 
+Hybrid 
+0.178 
+0.178 
+0.34 
+0.07 
+0.64 
+0.91 
+0.66 
+Demog 
+0.151 
+0.151 
+0.72 
+0.57 
+0.63 
+0.90 
+0.66 
+ 
+
+30 
+ 
+ 
+We can see these results in a bar chart where a min max scaler has been applied. This basically 
+shows which model wins in each category. 
+ 
+Figure 9 Scaled metrics for both models. 
+ 
+We can see that the hybrid model loses to the demographic model in coverage and 
+personalization and has higher values in the other metrics. However, we can see that results are 
+virtually equal in terms of Diversity and Novelty, and only on the Precision and Recall do we see 
+larger values for the hybrid model, which are not that much higher. On the other hand, the 
+demographic recommender has much larger personalization and coverage. Here we can see an 
+increment by the demographic model compared to the hybrid model. This makes sense because 
+the demographic model is more complex in how recommendations are given by finding similar 
+users in terms of demographic features and then recommending similar items to the user on a 
+more individual basis, whereas the hybrid model is again based on high level preferences.    
+ 
+Table 11 Values for the various metrics on the hybrid phase 2 and hybrid phase 3 model recommendations. 
+ 
+MAP@K MAR@K 
+Coverage 
+Personalization 
+Diversity HL 
+Diversity LL 
+Novelty 
+Hybrid 
+P2 
+0.219 
+0.219 
+0.17 
+1.11e-16 
+0.64 
+0.91 
+0.66 
+Hybrid 
+P3 
+0.178 
+0.178 
+0.34 
+0.07 
+0.64 
+0.91 
+0.66 
+ 
+
+MAP@K
+MAR@K
+Coverage
+Personalization
+Diversity HL
+Diversity LL
+Novelty31 
+ 
+It is also interesting to compare the metrics between the hybrid in phase 2 and phase 3. We can 
+see that most metrics remain similar with a slight decrease in precision and recall, which may be 
+just random, a slight increase in personalization, and a rather large increase in coverage. This 
+can be due to more items recommended and not filtered out due to poor ratings because of the 
+existence of more users and ratings on items. It is interesting to see a variation of the metrics of 
+the same recommender as the amount of data increases. 
+ 
+4.3.4 CS in Phase 4 
+Phase 4 starts when a given number of users and a given density of the user-item rating DF is 
+achieved. When this happens, the final recommender is initiated. This recommender is the 
+already mentioned FFM. In phase 4, the recommendations are, once again, the result of an 
+ensemble of recommenders, the same one in phase 3 with the addition of the new FFM. The 
+resulting metrics are once more applied to the recommendations and are shown in the following 
+table. In this phase we have 250 users and 191 ratings. 
+ 
+Table 12 Values for the various metrics on the hybrid, demographic and collaborative model 
+recommendations. 
+ 
+MAP@K 
+MAR@K 
+Coverage 
+Personalization 
+Diversity HL 
+Diversity LL 
+Novelty 
+Hybrid 
+0.158 
+0.158 
+0.34 
+0.06 
+0.64 
+0.91 
+0.66 
+Demog 
+0.137 
+0.137 
+0.68 
+0.55 
+0.66 
+0.91 
+0.66 
+Collab 
+0.181 
+0.181 
+0.72 
+0.54 
+0.67 
+0.91 
+0.66 
+ 
+Comparing the recommenders, we can observe that the collaborative recommender, which was 
+added in this later stage has high levels of personalization and coverage and achieves the highest 
+values for precision and recall, compared to the other two models. The values for diversity are all 
+similar at this stage, and novelty again doesn’t provide useful information  ith this number of total 
+items. In terms of precision and recall, coverage and personalization, the collaborative 
+recommender gives us expected results which is relatively high values in these metrics. We can 
+observe that each recommender brings different recommendations to the table with clear 
+improvements in some metrics as the recommender system matures. It would be interesting to 
+view this with a dataset comprising many more items and users. In the following figure we can 
+see the metrics in a scaled graph. 
+ 
+
+32 
+ 
+ 
+Figure 10 Scaled metrics for all three models 
+ 
+As said, we observe that the collaborative metrics are good in comparison to the other two, 
+however, the collaborative model is only useful when the recommender system has seen 
+sufficient data. The metrics for the other t o are not as high but they don’t suffer so much from 
+cold-start issues. We can see that between the demographic and the hybrid models there is a 
+trade-off in metrics. We had already seen this in the previous phase. 
+ 
+Table 13 Values for the various metrics on the phase 1, phase 2 and phase 3 model recommendations of 
+hybrid and demographic models. 
+ 
+MAP@K 
+MAR@K 
+Coverage 
+Personalization 
+Diversity HL 
+Diversity LL 
+Novelty 
+Hybrid 
+P2 
+0.219 
+0.219 
+0.17 
+1.11e-16 
+0.64 
+0.91 
+0.66 
+Hybrid 
+P3 
+0.178 
+0.178 
+0.34 
+0.07 
+0.64 
+0.91 
+0.66 
+Hybrid 
+P4 
+0.158 
+0.158 
+0.34 
+0.06 
+0.64 
+0.91 
+0.66 
+Demog 
+P3 
+0.151 
+0.151 
+0.72 
+0.57 
+0.63 
+0.90 
+0.66 
+Demog 
+P4 
+0.137 
+0.137 
+0.68 
+0.55 
+0.66 
+0.91 
+0.66 
+ 
+
+MAP@K
+MAR@K
+Coverage
+Personalization
+Diversity HL
+Diversity LL
+Novelty33 
+ 
+Here we can see a comparison between the metrics of the different models along each phase, 
+we can see a slight decrease of precision and recall in the evolving phases for hybrid and 
+demographic models, but this might have to do with insufficient ratings being added between 
+phase 3 and phase 4, which are important for the demographic recommender. With a further 
+increase in data, we can see further differences in the metrics. Feeding the recommender system 
+with 1000 users and 883 ratings, we attain the following results. 
+ 
+Table 14 Values for the various metrics on the hybrid, demographic and collaborative model 
+recommendations, in the case of 250 users and 191 ratings as well as 1000 users and 883 ratings. 
+ 
+MAP@K 
+MAR@K 
+Coverage 
+Personalization 
+Diversity HL 
+Diversity LL 
+Novelty 
+Hybrid 
+0.158 
+0.158 
+0.34 
+0.06 
+0.64 
+0.91 
+0.66 
+Demog 
+0.137 
+0.137 
+0.68 
+0.55 
+0.66 
+0.91 
+0.66 
+Collab 
+0.181 
+0.181 
+0.72 
+0.54 
+0.67 
+0.91 
+0.66 
+Hybrid 
+1000 
+0.088 
+0.088 
+0.28 
+0.19 
+0.69 
+0.89 
+0.66 
+Demog 
+1000 
+0.128 
+0.128 
+0.97 
+0.59 
+0.48 
+0.89 
+0.66 
+Collab 
+1000 
+0.119 
+0.119 
+0.79 
+0.61 
+0.52 
+0.89 
+0.66 
+ 
+ 
+ 
+Figure 11 Scaled metrics for all three models. 
+
+MAP@K
+MAR@K
+Coverage
+Personalization
+Diversity HL
+Diversity LL
+Novelty34 
+ 
+We can see that the metrics are qualitatively similar to the case before with less users and ratings. 
+Still the number of ratings is low, there is not a lot of rating density, which particularly penalizes 
+the collaborative model. Nonetheless, we can observe that the collaborative model is the one that 
+offers more personalization, which increased for all models with the increment in users and 
+ratings. Coverage also increased heavily for the demographic model while only increasing slightly 
+for the collaborative model. As for precision and recall, the demographic model maintains the 
+metric with only a slight decrease while the hybrid and collaborative model saw a rather significant 
+decrease. In regard to the collaborative model this might have to do with the low density in ratings. 
+All in all we see that the demographic and collaborative models clearly become more dominant 
+and useful as more data is added to the RS. The phases also make sense, by having the 
+collaborative model initiate after all others have been initiated, since the collaborative model is 
+very sensitive to rating density, while the demographic model is more robust in that sense. The 
+hybrid model by this phase has clearly been passed by the two other models in most metrics 
+which is exactly what would be expected.  
+ 
+5 
+Conclusion and future works 
+In this work an ontology-based context aware recommender system application for tourism was 
+presented where different recommenders are used at different stages of maturity of the 
+recommender system. The novel aspect is the evolution of the recommender system with different 
+types of recommenders entering the recommendation pool as the system’s maturity evolves. The 
+ontology extension of the recommender system allows items to be binned and recommended to 
+users based on user preference vectors with different degrees of detail that link to the item 
+ontology. These preference vectors will be ever changing based on user feedback, while other 
+recommenders based on demographic features and field-aware factorization machines join the 
+pool as data increases.  
+Along this work, the RS was presented and ultimately tested with synthetic data mimicking 
+different stages of maturity. One could observe that at each new phase the new recommenders 
+added value as observed from the comparison between the different adopted metrics, which were 
+MAP@K, MAR@K, Coverage, Personalization, Diversity HL, Diversity LL and finally Novelty. 
+These metrics are the state of the art for Recommender Systems because they attempt to go 
+beyond the usual metrics adopted in   ,  hich don’t al ays have much meaning in RS. The 
+results obtained were expected where Collaborative and Demographic approaches essentially 
+brought more personalization and coverage to the table. However, the full extent of differences 
+between recommenders could not be captured mainly due to the relatively low cardinality of items 
+being offered, only 29. 
+Future works would entail a broader analysis with more items, and also context-aware data which 
+was not tested at this instance. Nonetheless, the context-aware would be essentially pre-filtering 
+which would not be of much interest regarding the results concerning the metrics. 
+
+35 
+ 
+6 
+Acknowledgements 
+The present paper was developed in the context of the PMP project – Partnership Management 
+Platform, code LISBOA-01-0247-FEDER-045411, co-financed by LISBOA 2020 and Portugal 
+2020 through the European Regional Development Fund. 
+ 
+7 
+References 
+ 
+[1] 
+C. I.  ee,  . C.  sia,  . C.  su, and J. Y.  in, “ ntology-based tourism recommendation 
+system,” 2017 4th International Conference on Industrial Engineering and Applications, 
+ICIEA 2017, pp. 376–379, 2017, doi: 10.1109/IEA.2017.7939242. 
+[2] 
+J. Borràs, A. Moreno, and A.  alls, “Intelligent tourism recommender systems: A survey,” 
+Expert Systems with Applications, vol. 41, no. 16. Elsevier Ltd, pp. 7370–7389, Nov. 15, 
+2014. doi: 10.1016/j.eswa.2014.06.007. 
+[3] 
+ . K a ,  .  a hchoune, and  .  ahab, “ ourism Recommender Systems: An Overview 
+of Recommendation Approaches,” International Journal of Computer Applications, vol. 
+180, no. 20, pp. 9–13, 2018, doi: 10.5120/ijca2018916458. 
+[4] 
+A. Montejo-Ráez, J. M. Perea-Ortega, M. Á. García-Cumbreras, and F. Martínez-
+Santiago, “ tiûm: A  eb based planner for tourism and leisure,” Expert Systems with 
+Applications, 
+vol. 
+38, 
+no. 
+8, 
+pp. 
+10085–10093, 
+Aug. 
+2011, 
+doi: 
+10.1016/j.eswa.2011.02.005. 
+[5] 
+I. Garcia,  . Sebastia, and  .  naindia, “ n the design of individual and group 
+recommender systems for tourism,” Expert Systems with Applications, vol. 38, no. 6, pp. 
+7683–7692, 2011, doi: 10.1016/j.eswa.2010.12.143. 
+[6] 
+ . Khallou i, A. Abatal, and  .  ahaj, “An ontology-based context awareness for smart 
+tourism recommendation system,”  ay 20 8. doi:  0.  45/3230905.3230935. 
+[7] 
+A.  . Kashevni , A. v  onomarev, and A. v Smirnov, “I     IG  C  A  ultimodel 
+Context-A are  ourism Recommendation Service : Approach and Architecture,” vol. 56, 
+no. 2, pp. 245–258, 2017, doi: 10.1134/S1064230717020125. 
+[8] 
+A.  oreno, A.  alls,  . Isern,  .  arin, and J.  orràs, “Sig ur/E-Destination: Ontology-
+based personali ed recommendation of  ourism and  eisure Activities,” Engineering 
+Applications of Artificial Intelligence, vol. 26, no. 1, pp. 633–651, Jan. 2013, doi: 
+10.1016/j.engappai.2012.02.014. 
+
+36 
+ 
+[9] 
+M. Nilashi, K. Bagherifard,  . Rahmani, and  . Rafe, “A recommender system for tourism 
+industry using cluster ensemble and prediction machine learning techni ues,” Computers 
+and Industrial Engineering, vol. 109, pp. 357–368, 2017, doi: 10.1016/j.cie.2017.05.016. 
+[10] 
+M. Nilashi, K.  agherifard,  . Rahmani, and  . Rafe, “A recommender system for tourism 
+industry using cluster ensemble and prediction machine learning techni ues,” Computers 
+and Industrial Engineering, vol. 109, 2017, doi: 10.1016/j.cie.2017.05.016. 
+[11] 
+Á. García-Crespo, J. L. López-Cuadrado, R. Colomo-Palacios, I. González-Carrasco, and 
+B. Ruiz- e cua, “Sem-Fit: A semantic based expert system to provide recommendations 
+in the tourism domain,” Expert Systems with Applications, vol. 38, no. 10, pp. 13310–
+13319, Sep. 2011, doi: 10.1016/j.eswa.2011.04.152. 
+[12] 
+ .  ilashi,  . bin Ibrahim,  . Ithnin, and  .  . Sarmin, “A multi-criteria collaborative 
+filtering recommender system for the tourism domain using Expectation Maximization 
+(EM) and PCA-A  IS,” Electronic Commerce Research and Applications, vol. 14, no. 6, 
+pp. 542–562, Oct. 2015, doi: 10.1016/j.elerap.2015.08.004. 
+[13] 
+J. Borràs et al., “Sig ur/ -Destination: A System for the Management of Complex Tourist 
+Regions,” in Information and Communication Technologies in Tourism 2011, 2011, pp. 
+39–50. doi: 10.1007/978-3-7091-0503-0_4. 
+[14] 
+C. Grün, J.  eidhardt, and  .  erthner, “ ntology-Based Matchmaking to Provide 
+ ersonali ed Recommendations for  ourists,” in Information and Communication 
+Technologies in Tourism 2017, Springer International Publishing, 2017, pp. 3–16. doi: 
+10.1007/978-3-319-51168-9_1. 
+[15] 
+Y. Huang and L. Bian, “A  ayesian net or  and analytic hierarchy process based 
+personali ed recommendations for tourist attractions over the Internet,” Expert Systems 
+with Applications, vol. 36, no. 1, pp. 933–943, 2009, doi: 10.1016/j.eswa.2007.10.019. 
+[16] 
+J. Beel, C. Breitinger, S.  anger, A.  ommat sch, and  . Gipp, “ o ards reproducibility in 
+recommender-systems research,” User Modeling and User-Adapted Interaction, vol. 26, 
+no. 1, pp. 69–101, Mar. 2016, doi: 10.1007/s11257-016-9174-x. 
+[17] 
+J. J. Carroll, D. Reynolds, I.  ic inson, A. Seaborne, C.  ollin, and K.  il inson, “Jena: 
+Implementing the semantic  eb recommendations,” in Proceedings of the 13th 
+International World Wide Web Conference on Alternate Track, Papers and Posters, WWW 
+Alt. 2004, May 2004, pp. 74–83. doi: 10.1145/1013367.1013381. 
+[18] 
+C.  ouras and  .  sog as, “Improving ne s articles recommendations via user 
+clustering,” International Journal of Machine Learning and Cybernetics, vol. 8, no. 1, pp. 
+223–237, Feb. 2017, doi: 10.1007/s13042-014-0316-3. 
+[19] 
+P. Sit rong ong, S.  aneeroj,  . Samatthiyadi un, and A.  a asu, “ ayesian probabilistic 
+model for context-a are recommendations,” 17th International Conference on Information 
+
+37 
+ 
+Integration and Web-Based Applications and Services, iiWAS 2015 - Proceedings, 2015, 
+doi: 10.1145/2837185.2837223. 
+[20] 
+ .  asid and R. Ali, “Context Similarity  easurement  ased on Genetic Algorithm for 
+Improved Recommendations,” Applications of Soft Computing for the Web, pp. 11–29, 
+2017, doi: 10.1007/978-981-10-7098-3_2. 
+[21] 
+Y. Zheng,  .  obasher, and R.  ur e, “Context recommendation using multi-label 
+classification,” Proceedings - 2014 IEEE/WIC/ACM International Joint Conference on Web 
+Intelligence and Intelligent Agent Technology - Workshops, WI-IAT 2014, vol. 2, no. May, 
+pp. 288–295, 2014, doi: 10.1109/WI-IAT.2014.110. 
+[22] 
+ . Shin, J.  .  ee, J. Yeon, and S. G.  ee, “Context-aware recommendation by 
+aggregating user context,” 2009 IEEE Conference on Commerce and Enterprise 
+Computing, CEC 2009, pp. 423–430, 2009, doi: 10.1109/CEC.2009.38. 
+[23] 
+Y. Gu, J. Song,  .  iu,  . Zou, and Y. Yao, “CA  : Context A are  atrix  actori ation 
+for Social Recommendation,” Web Intelligence, vol. 16, no. 1, pp. 53–71, 2018, doi: 
+10.3233/WEB-180373. 
+[24] 
+G. Adomavicius and A.  u hilin, “Context-a are recommender systems,” Recommender 
+Systems Handbook, Second Edition, pp. 191–226, 2015, doi: 10.1007/978-1-4899-7637-
+6_6. 
+[25] 
+R.  ur e, A.  elfernig, and  .  . Gö er, “Recommender Systems: An  vervie ,” 20  , 
+[Online]. Available: www.aaai.org 
+[26] 
+ .  . Knijnenburg and  . C.  illemsen, “ valuating recommender systems  ith user 
+experiments,” Recommender Systems Handbook, Second Edition, pp. 309–352, 2015, 
+doi: 10.1007/978-1-4899-7637-6_9. 
+[27] 
+R. Irfan et al., “ obiContext: A Context-Aware Cloud-Based Venue Recommendation 
+ rame or ,” IEEE Transactions on Cloud Computing, vol. 5, no. 4, pp. 712–724, 2015, 
+doi: 10.1109/tcc.2015.2440243. 
+[28] 
+G. Adomavicius,  .  obasher,  . Ricci, and A.  u hilin, “Context-Aware Recommender 
+Systems,” AI Magazine, vol. 32, no. 3, p. 67, Oct. 2011, doi: 10.1609/aimag.v32i3.2364. 
+[29] 
+J.  iu, C.  u, and  .  iu, “ ayesian probabilistic matrix factori ation  ith social relations 
+and item contents for recommendation,” Decision Support Systems, vol. 55, no. 3, pp. 
+838–850, 2013, doi: 10.1016/j.dss.2013.04.002. 
+[30] 
+R.  ur e, “ ybrid Recommender Systems: Survey and  xperiments,” User Modeling and 
+User-Adapted Interaction, vol. 12, no. 4, pp. 331–370, 2002, [Online]. Available: 
+http://www.springerlink.com/openurl.asp?id=doi:10.1023/A:1021240730564%5Cnpapers
+2://publication/doi/10.1023/A:1021240730564 
+
+38 
+ 
+[31] 
+ .  agci and  . Karago , “Context-aware location recommendation by using a random 
+walk-based approach,” Knowledge and Information Systems, vol. 47, no. 2, pp. 241–260, 
+2016, doi: 10.1007/s10115-015-0857-0. 
+[32] 
+S. Kul arni and S.  . Rodd, “Context A are Recommendation Systems: A revie  of the 
+state of the art techni ues,” Computer Science Review, vol. 37, p. 100255, 2020, doi: 
+10.1016/j.cosrev.2020.100255. 
+[33] 
+ . Chen and Y.  . Chuang, “ u  y and nonlinear programming approach for optimi ing 
+the performance of ubi uitous hotel recommendation,” Journal of Ambient Intelligence and 
+Humanized Computing, vol. 9, no. 2, pp. 275–284, Apr. 2018, doi: 10.1007/s12652-015-
+0335-2. 
+[34] 
+Kha aei and Alimohammadi, “Context-Aware Group-Oriented Location Recommendation 
+in Location- ased Social  et or s,” ISPRS International Journal of Geo-Information, vol. 
+8, no. 9, p. 406, 2019, doi: 10.3390/ijgi8090406. 
+[35] 
+ . Gabor and  . Altmann, “ enchmar ing Surrogate-Assisted Genetic Recommender 
+Systems,” 20 9, [ nline]. Available: http://arxiv.org/abs/ 908.02880 
+[36] 
+ . Khalid,  .  . S. Khan, S.  . Khan, and A. Y. Zomaya, “ mniSuggest: A ubi uitous 
+cloud-based context-a are recommendation system for mobile social net or s,” IEEE 
+Transactions on Services Computing, vol. 7, no. 3, pp. 401–414, 2014, doi: 
+10.1109/TSC.2013.53. 
+[37] 
+M. H. Kuo,  . C. Chen, and C.  .  iang, “ uilding and evaluating a location-based service 
+recommendation system  ith a preference adjustment mechanism,” Expert Systems with 
+Applications, 
+vol. 
+36, 
+no. 
+2 
+PART 
+2, 
+pp. 
+3543–3554, 
+2009, 
+doi: 
+10.1016/j.eswa.2008.02.014. 
+[38] 
+Y.  ang and Y. Guo, “A context-a are matrix factori ation recommender algorithm,” 
+Proceedings of the IEEE International Conference on Software Engineering and Service 
+Sciences, ICSESS, pp. 914–918, 2013, doi: 10.1109/ICSESS.2013.6615454. 
+[39] 
+M. Sadeghi and S. A. Asghari, “Recommender Systems  ased on  volutionary 
+Computing: A Survey,” Journal of Software Engineering and Applications, vol. 10, no. 05, 
+pp. 407–421, 2017, doi: 10.4236/jsea.2017.105023. 
+[40] 
+ .  .  ao, S. R. Jeong, and  . Ahn, “A novel recommendation model of location-based 
+advertising: Context-A are Collaborative  iltering using GA approach,” Expert Systems 
+with Applications, vol. 39, no. 3, pp. 3731–3739, 2012, doi: 10.1016/j.eswa.2011.09.070. 
+[41] 
+A. Livne, M. Unger, B. Shapira, and L. Ro ach, “ eep Context-Aware Recommender 
+System 
+ tili ing 
+Se uential 
+ atent 
+Context,” 
+20 9, 
+[ nline]. 
+Available: 
+http://arxiv.org/abs/1909.03999 
+
+39 
+ 
+[42] 
+ .  ossein adeh Aghdam, “Context-aware recommender systems using hierarchical 
+hidden  ar ov model,” Physica A: Statistical Mechanics and its Applications, vol. 518, pp. 
+89–98, 2019, doi: 10.1016/j.physa.2018.11.037. 
+[43] 
+N. M. Villegas, C. Sánchez, J. Díaz-Cely, and G.  amura, “Characteri ing context-aware 
+recommender systems: A systematic literature revie ,” Knowledge-Based Systems, vol. 
+140, pp. 173–200, 2018, doi: 10.1016/j.knosys.2017.11.003. 
+[44] 
+S. Ra a and C.  ing, “ rogress in context-aware recommender systems - An overvie ,” 
+Computer Science Review, vol. 31, pp. 84–97, 2019, doi: 10.1016/j.cosrev.2019.01.001. 
+[45] 
+J.  ian, Z. Chen, X. Zhou, X. Xie,  . Zhang, and G. Sun, “x eep  : Combining explicit 
+and implicit feature interactions for recommender systems,” Proceedings of the ACM 
+SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 1754–
+1763, 2018, doi: 10.1145/3219819.3220023. 
+[46] 
+S. Sivapalan, “A Genetic Algorithm Approach to Recommender System Cold Start 
+ roblem,” 20 5. 
+[47] 
+ . Alhija i, “ he  se of the Genetic Algorithms in the Recommender Systems,” no.  arch, 
+2017, doi: 10.13140/RG.2.2.24308.76169. 
+[48] 
+J. Rajes ari and S.  ariharan, “ ersonali ed Search Recommender System: State of Art, 
+ xperimental Results and Investigations,” International Journal of Education and 
+Management 
+Engineering, 
+vol. 
+6, 
+no. 
+3, 
+pp. 
+1–8, 
+May 
+2016, 
+doi: 
+10.5815/ijeme.2016.03.01. 
+[49] 
+ .   ivedi and K. K.  harad aj, “A fu  y approach to multidimensional context aware e-
+learning recommender system,” Lecture Notes in Computer Science (including subseries 
+Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8284 
+LNAI, pp. 600–610, 2013, doi: 10.1007/978-3-319-03844-5_59. 
+[50] 
+S.  .  in and I.  an, “ etection of the customer time-variant pattern for improving 
+recommender systems,” Expert Systems with Applications, vol. 28, no. 2, pp. 189–199, 
+2005, doi: 10.1016/j.eswa.2004.10.001. 
+[51] 
+ .  ernando and  .  amayo, “Smart articipation A Fuzzy-Based Recommender System 
+for Political Community- uilding,” 20 4. 
+[52] 
+A. Ciaramella,  . G. C. A. Cimino,  .  a  erini, and  .  arcelloni, “ sing context history 
+to personali e a resource recommender via a genetic algorithm,” Proceedings of the 2010 
+10th International Conference on Intelligent Systems Design and Applications, ISDA’10, 
+pp. 965–970, 2010, doi: 10.1109/ISDA.2010.5687064. 
+[53] 
+ .  ouneffouf, A.  ou eghoub, and A.  . Gançars i, “A contextual-bandit algorithm for 
+mobile context-a are recommender system,” Lecture Notes in Computer Science 
+
+40 
+ 
+(including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in 
+Bioinformatics), vol. 7665 LNCS, no. PART 3, pp. 324–331, 2012, doi: 10.1007/978-3-
+642-34487-9_40. 
+[54] 
+R. Meena and K. K.  harad aj, “A Genetic Algorithm Approach for Group Recommender 
+System  ased on  artial Ran ings,” Journal of Intelligent Systems, vol. 29, no. 1, pp. 653–
+663, 2020, doi: 10.1515/jisys-2017-0561. 
+[55] 
+J. A. Konstan and G. Adomavicius, “ o ard identification and adoption of best practices 
+in algorithmic recommender systems research,” in ACM International Conference 
+Proceeding Series, 2013, pp. 23–28. doi: 10.1145/2532508.2532513. 
+[56] 
+ . Zheng and Q.  i, “A recommender system based on tag and time information for social 
+tagging systems,” Expert Systems with Applications, vol. 38, no. 4, pp. 4575–4587, 2011, 
+doi: 10.1016/j.eswa.2010.09.131. 
+[57] 
+M. A. Domingues, A. M. Jorge, and C. Soares, “ imensions as  irtual Items: Improving 
+the predictive ability of top-  recommender systems,” Information Processing and 
+Management, vol. 49, no. 3, pp. 698–720, 2013, doi: 10.1016/j.ipm.2012.07.009. 
+[58] 
+L. O. Colombo-Mendoza, R. Valencia-García, A. Rodríguez-González, G. Alor-
+Hernández, and J. J. Samper-Zapater, “Recom et : A context-aware knowledge-based 
+mobile recommender system for movie sho times,” Expert Systems with Applications, vol. 
+42, no. 3, pp. 1202–1222, 2015, doi: 10.1016/j.eswa.2014.09.016. 
+[59] 
+M. Y. H. Al-Shamri and K. K.  harad aj, “ u  y-genetic approach to recommender 
+systems based on a novel hybrid user model,” Expert Systems with Applications, vol. 35, 
+no. 3, pp. 1386–1399, 2008, doi: 10.1016/j.eswa.2007.08.016. 
+[60] 
+S. Renjith, A. Sree umar, and  . Jathavedan, “An extensive study on the evolution of 
+context-a are personali ed travel recommender systems,” Information Processing and 
+Management, vol. 57, no. 1, p. 102078, 2020, doi: 10.1016/j.ipm.2019.102078. 
+[61] 
+U. Marung, N. Theera- mpon, and S. Auephan iriya ul, “ op-N recommender systems 
+using genetic algorithm-based visual-clustering methods,” Symmetry (Basel), vol. 8, no. 
+7, pp. 1–19, 2016, doi: 10.3390/sym8070054. 
+[62] 
+ .  ohamed,  . Abdulsalam, and  .  ohammed, “Adaptive genetic algorithm for 
+improving prediction accuracy of a multi-criteria recommender system,” Proceedings - 
+2018 IEEE 12th International Symposium on Embedded Multicore/Many-Core Systems-
+on-Chip, MCSoC 2018, vol. 11, pp. 79–86, 2018, doi: 10.1109/MCSoC2018.2018.00025. 
+[63] 
+Y. Kilani, A.  .  toom, A. Alsarhan, and  . Almaayah, “A genetic algorithms-based hybrid 
+recommender system of matrix factorization and neighborhood-based techni ues,” 
+Journal 
+of 
+Computational 
+Science, 
+vol. 
+28, 
+pp. 
+78–93, 
+2018, 
+doi: 
+10.1016/j.jocs.2018.08.007. 
+
+41 
+ 
+[64] 
+Y. Juan, Y. Zhuang,  . S. Chin, and C. J.  in, “ ield-aware factorization machines for 
+C R prediction,” RecSys 2016 - Proceedings of the 10th ACM Conference on 
+Recommender Systems, pp. 43–50, 2016, doi: 10.1145/2959100.2959134. 
+[65] 
+J. M. Ruiz-Martínez, J. A. Miñarro-Giménez, D. Castellanos-Nieves, F. García-Sáanchez, 
+and R. Valencia-García, “ ntology population: An application for the  -tourism domain,” 
+International Journal of Innovative Computing, Information and Control, vol. 7, no. 11, pp. 
+6115–6183, 2011. 
+[66] 
+R.  arta, C.  eilmayr,  .  röll, C. Grün, and  .  erthner, “Covering the semantic space 
+of tourism : An approach based on modulari ed ontologies,” in ACM International 
+Conference Proceeding Series, 2009, p. 79. doi: 10.1145/1552262.1552263. 
+[67] 
+K. Haruna et al., “Context-aware recommender system: A review of recent developmental 
+process and future research direction,” Applied Sciences (Switzerland), vol. 7, no. 12, pp. 
+1–25, 2017, doi: 10.3390/app7121211. 
+[68] 
+S.  inda and K. K.  harad aj, “A Genetic Algorithm Approach to Context-Aware 
+Recommendations Based on Spatio-temporal Aspects,” vol. 77 , Springer Singapore, 
+2019, pp. 59–70. doi: 10.1007/978-981-10-8797-4_7. 
+[69] 
+S. Rendle, “ actori ation machines,” in Proceedings - IEEE International Conference on 
+Data Mining, ICDM, 2010, pp. 995–1000. doi: 10.1109/ICDM.2010.127. 
+  
+

9NE4T4oBgHgl3EQfdgy1/vector_store/index.faiss

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:bb9fc27d56756712e6c800b61b43082afbb2b815f08bc3bfb08636a5350de9e5
+size 4128813

9tFLT4oBgHgl3EQfCC72/content/2301.11974v1.pdf

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:32d2d8b0b7d70a2379732eb344eafa3ff4fd590706a889e660c132ddb973be33
+size 339789

AdFLT4oBgHgl3EQfEy_H/vector_store/index.faiss

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:06223c0b4d312a337e0db5702afe1bf3f58346735ac440db6f7c8538052615c7
+size 12189741

B9AzT4oBgHgl3EQfwP5n/content/tmp_files/2301.01719v1.pdf.txt

@@ -0,0 +1,393 @@
+Radiance Textures for Rasterizing Ray-Traced Data
+Jakub Maksymilian Fober
+[email protected]
+Abstract
+Presenting real-time rendering of 3D surfaces using radiance
+textures for fast synthesis of complex incidence-variable ef-
+fects and environment interactions. This includes iridescence,
+parallax occlusion and interior mapping, (specular, regular,
+diffuse, total-internal) reflections with many bounces, re-
+fraction, subsurface scattering, transparency, and possibly
+more. This method divides textures into a matrix of radiance
+buckets, where each bucket represent some data at various
+incidence angles. Data can show final pixel color, or deferred
+rendering ambient occlusion, reflections, shadow map, etc.
+Resolution of the final synthesized output is the radiance
+bucket matrix size. Technique can be implemented with a
+simple fragment shader. The computational footprint of this
+technique is of simple diffuse-only graphics, but with vi-
+sual fidelity of complex (off-line) ray-traced render at the
+cost of storage memory footprint. Balance between com-
+putational footprint and storage memory footprint can be
+easily achieved with variable compression ratio of repetitive
+radiance scene textures.
+CCS Concepts: • Computing methodologies → Reflectance
+modeling; Rasterization; Texturing; Ray tracing.
+Keywords: 3D graphics, holography, light field, plenoptic,
+radiance field, rasterization, ray tracing, reflectance field
+© 2023 Jakub Maksymilian Fober
+This work is licensed under Creative Commons BY-NC-ND 3.0 license.
+https://creativecommons.org/licenses/by-nc-nd/3.0/
+For all other uses including commercial, contact the owner/author(s).
+1
+Introduction
+Radiance and reflectance field rendering techniques are a
+class of algorithms used in computer graphics to generate im-
+ages of three-dimensional scenes. These algorithms simulate
+the way light interacts with surfaces in a virtual environment,
+producing realistic and detailed images.
+These techniques have been the subject of extensive re-
+search in computer graphics and rendering, as they offer a
+powerful and flexible way to generate high-quality images.
+There is a wide range of applications for radiance and re-
+flectance field algorithms, including film and video game
+production, architectural visualization, and scientific visual-
+ization.
+In this paper, technique is presented to capture and render
+complex precomputed light interactions, via radiance field
+textures, embedded onto three-dimensional-object’s surface.
+The presented technique utilizes a standard fragment pixel
+shader and a two-dimensional texture lookup to render dy-
+namic, view-independent, photo-realistic images at a fraction
+of the computational cost associated with effects such as real-
+time ray tracing, parallax mapping, and dynamic shadowing.
+It is well-suited for real-time execution in video games,
+virtual reality, and virtual production environments on mod-
+ern hardware. It can take advantage of the direct storage
+capability in ninth-generation gaming systems, providing
+high-fidelity, high-performance images.
+This technique can replace computationally heavy rendering-
+pipeline chains, while preserving hardware-accelerated, highly-
+optimized rasterization elements. It can also enable wider
+implementation of real-time GPU ray-tracing, with ability
+to combine bounce rays with precomputed radiance of the
+environment.
+1.1
+Previous work
+Mainstream implementations of radiance field rendering
+focus on volumetric data structures and spherical harmonics
+for rendering images[Yu et al. 2021]. While volumetric data
+can be sparse in order to exclude void regions[Yu et al. 2021],
+the ultimate goal would logically be to perfectly match the
+geometry of the represented object. And since the inside
+volume of the object is of no interest (most of the time), only
+half of the radiance sphere is considered practically useful.
+Therefore, such fields could effectively be spread across the
+surface of the object.
+Some researchers embraced this approach, with neural
+reflectance fields as texturing primitives[Baatz et al. 2022],
+which rendered high-fidelity results. But while neural fields
+produce fantastic results, they are computationally inten-
+sive at rendering time[Yu et al. 2021] and therefore are not
+suitable for real-time applications.
+1.2
+Overview of the content
+In this initial version of paper you will find theoretical ex-
+planation and implementation of the subject, along with
+equations and schematics. Some elements had been tested,
+like mapping functions, some yet to be presented, as the
+follow-up updates continue.
+1.3
+Document naming convention
+This document uses the following naming convention:
+• Left-handed coordinate system.
+arXiv:2301.01719v1  [cs.GR]  4 Jan 2023
+
+Fober, J.M.
+• Vectors presented natively in column.
+• Row-major order matrix arranged, denoted “𝑀row col”.
+• Matrix multiplication by “[column]𝑎 · [row]𝑏 = 𝑀𝑎 𝑏”.
+• A single bar enclosure “|𝑢|” represents scalar absolute.
+• A single bar enclosure “|�𝑣|” represents vector’s length.
+• Vectors with an arithmetic sign, or without, are calcu-
+lated component-wise and form another vector.
+• Centered dot “·” represents the vector dot product.
+• Square brackets with a comma “[𝑓 ,𝑐]” denote interval.
+• Square brackets with blanks “[𝑥 𝑦]” denote vectors
+and matrices.
+• The power of “−1” implies the reciprocal of the value.
+• QED symbol “□” marks the final result or output.
+This naming convention simplifies the process of transform-
+ing formulas into shader code.
+2
+Methodology
+Each pixel of the model’s texture contains discrete radiance
+hemispherical map of size 𝑛 ×𝑛, called “bucket”. Buckets are
+arranged in place of initial texture’s pixels, increasing overall
+resolution to 𝑤 ·𝑛 ×ℎ ·𝑛 pixels, where 𝑤 and ℎ denote width
+and height of the synthesized output texture, respectively.
+Buckets are highly repetitive and change only slightly from
+one to another. This is a great case for a simple compression.
+To synthesize output texture for a given view position,
+single sample per bucket is taken, giving normal resolution
+texture output.
+Model’s 𝑢, 𝑣 texture coordinates correspond to bucket ma-
+trix position index, while incidence vector, correspond to
+bucket’s internal 𝑢, 𝑣 position. Therefore radiance texture
+sampling algorithm can be described as a four-dimensional
+plenoptic function 𝐿(𝑢, 𝑣,𝜃,𝜙), where 𝑢, 𝑣 denote model’s
+texture coordinates and 𝜃,𝜙 incidence angles.
+Figure 1. Radiance texture sampling model, where the inci-
+dence R3 vector (blue) is projected and squarified (orange)
+to R2 texture coordinates (red and green), which map onto
+hemispherical radiance bucket represented as a flat square.
+Each radiance bucket should represent a hemisphere of
+reflectivity. Equisolid azimuthal projection was chosen for
+this task, for its properties, as it preserves area and resem-
+bles spherical mirror reflection[Wikipedia contributors 2022].
+Resolution of the radiance bucket, in such projection, directly
+corresponds to sin(𝜃/2)
+√
+2, where 𝜃 is the incidence angle.
+To efficiently spread information across square buckets, ad-
+ditional disc-to-square mapping function was implemented,
+providing uniform pixel count across both orthogonal direc-
+tions and diagonal directions.
+Equisolid azimuthal projection mapping can be easily im-
+plemented in the vector domain without the use of anti-
+trigonometric functions, as the orthographically projected
+normalized sum of the incidence and normal vectors has
+a length of sin(𝜃/2). This eliminates 𝜃,𝜙 angles from the
+plenoptic function, resulting in new 𝐿′(𝑢, 𝑣,𝑥,𝑦,𝑧), where
+𝑥,𝑦,𝑧 correspond to incidence unit-vector components in
+orthogonal texture space.
+2.1
+Mapping of incident vector to radiance bucket
+For every visible pixel there is an incidence vector ˆ𝐼 ∈ R3.
+This vector can be mapped and projected to R2 texture coor-
+dinates using translation and R2×3-matrix transformation.
+Following equation maps incidence vector to azimuthal
+equisolid projection, with 𝑟 = 1, at Ω = 180°.
+
+�𝐴𝑥
+�𝐴𝑦
+√
+2 cos 𝜃/2
+
+=
+√
+2
+������
+
+ˆ𝐼𝑥 + ˆ𝑁𝑥
+ˆ𝐼𝑦 + ˆ𝑁𝑦
+ˆ𝐼𝑧 + ˆ𝑁𝑧
+
+������
+(1a)
+� �𝐴𝑥
+�𝐴𝑦
+�
+=
+√
+2
+���ˆ𝐼𝑥
+ˆ𝐼𝑦
+ˆ𝐼𝑧 + 1
+���
+�ˆ𝐼𝑥
+ˆ𝐼𝑦
+�
+, if ˆ𝑁𝑧 = 1
+(1b)
+Inverse mapping:
+
+ˆ𝐴′
+𝑥
+ˆ𝐴′
+𝑦
+ˆ𝐴′
+𝑧
+
+=
+
+�𝐴𝑥
+√︁
+1/2
+�𝐴𝑦
+√︁
+1/2
+√︃
+1 −
+�𝐴2𝑥
+2 −
+�𝐴2𝑦
+2
+
+(2a)
+
+ˆ𝐼𝑥
+ˆ𝐼𝑦
+ˆ𝐼𝑧
+
+= 2
+���
+�
+ˆ𝐴′ · ˆ𝑁
+
+ˆ𝐴′
+𝑥
+ˆ𝐴′
+𝑦
+ˆ𝐴′
+𝑧
+
+−
+
+ˆ𝑁𝑥
+ˆ𝑁𝑦
+ˆ𝑁𝑧
+
+���
+�
++
+
+ˆ𝑁𝑥
+ˆ𝑁𝑦
+ˆ𝑁𝑧
+
+(2b)
+=
+
+�𝐴𝑥
+√︃
+2 − �𝐴2𝑥 − �𝐴2𝑦
+�𝐴𝑦
+√︃
+2 − �𝐴2𝑥 − �𝐴2𝑦
+1 − �𝐴2
+𝑥 − �𝐴2
+𝑦
+
+, if ˆ𝑁𝑧 = 1
+(2c)
+where �𝐴 ∈ [−1, 1]2 is the azimuthal equisolid projection
+coordinate. 𝜃 is the incidence angle. ˆ𝑁 ∈ R3 is the surface
+normal vector. As the incidence ˆ𝐼 ∈ R3 is mapped to or from
+orthogonal texture space, where ˆ𝑁𝑧 = 1, the transformation
+can take form of equation 1b and 2c.
+
+Radiance Textures for Rasterizing Ray-Traced Data
+Following equation transforms azimuthal projection vec-
+tor, into square coordinates, for the radiance bucket sam-
+pling.1
+� �𝐵𝑥
+�𝐵𝑦
+�
+=
+�� � �𝐴𝑥
+�𝐴𝑦
+� ��
+max �| �𝐴𝑥 |, | �𝐴𝑦|�
+� �𝐴𝑥
+�𝐴𝑦
+�
+if �𝐴𝑥 and �𝐴𝑦 ≠ 0
+(3)
+where �𝐵 ∈ [−1, 1]2 is the bucket’s centered texture coordi-
+nate and �𝐴 ∈ [−1, 1]2 is the azimuthal projection vector.
+Note. It is important to prevent pixel blending between
+edges of neighboring buckets. This can be done by clamping
+bucket coordinates to �𝐵 ∈ [𝐵−1
+res − 1, 1 − 𝐵−1
+res]2 range.
+Inverse transformation of bucked, centered coordinates
+�𝐵 ∈ R2 to azimuthal projection coordinates ˆ𝐴 ∈ R2 can be
+achieved with same, but inverted method.
+� �𝐴𝑥
+�𝐴𝑦
+�
+= max �| �𝐵𝑥 |, | �𝐵𝑦|�
+√︃
+�𝐵2𝑥 + �𝐵2𝑦
+� �𝐵𝑥
+�𝐵𝑦
+�
+(4a)
+
+ˆ𝑅𝑥
+ˆ𝑅𝑦
+ˆ𝑅𝑧
+
+=
+
+− �𝐴𝑥
+√︃
+2 − �𝐴2𝑥 − �𝐴2𝑦
+− �𝐴𝑦
+√︃
+2 − �𝐴2𝑥 − �𝐴2𝑦
+1 − �𝐴2
+𝑥 − �𝐴2
+𝑦
+
+(4b)
+where ˆ𝑅 ∈ R3 denotes equisolid reflection vector. This vector
+is used to sample ray-traced data onto radiance field texture.
+It is a version of the vector mirrored along the normal, found
+in equation 2c on the preceding page.
+3
+Results
+TBA
+4
+Conclusion
+I have theorized about possible implementation of radiance
+field texturing using modern hardware shading capabilities,
+and presented mathematical solution for executing such con-
+cept.
+Note. More conclusion are to be added, after the update to
+the paper.
+5
+Possible applications
+Radiance field texture sampling can replace shading pipeline
+or supplement it with enhanced effects. Some such effects
+include:
+Parallax interior mapping. This effect is used to mimic
+interior of a room, as seen through a window, or it can simu-
+late a portal to another place.
+Proxy meshes with parallax mapping. Radiance tex-
+ture with alpha mask can simulate more complex or furry
+objects bound inside a proxy mesh. Similarly to neural radi-
+ance fields texturing primitives[Baatz et al. 2022].
+1See figure 2 for visual reference.
+(a) Picture of one cent American coin.
+(b) One cent coin mapped to a rectangle, using equation 3.
+Figure 2. A visual example of disc to square mapping using
+the formulation found in equation 3.
+Reflections. Many light bounces can be combined into a
+single pixel of the radiance texture map. Dynamic objects
+can then sample such radiance field to obtain environment
+reflections. Also semi real-time ray-tracing can accumulate
+dynamically generated reflections into such texture map, to
+update and enhance environment one.
+Shadowing. 1-bit radiance field texture map can repre-
+sent shadowing of static objects. Here, incidence vector is
+replaced with light direction vector for shadow occlusion
+sampling. It can work with both parallel light sources and
+point lights. With more than one sample per bucket, area
+shadows are possible to produce.
+Subsurface scattering. This computationally demand-
+ing effect can be encoded in a radiance texture map, which
+then replaces incidence vector, with the light direction vector
+in relation to the view position for sampling.
+References
+H. Baatz, J. Granskog, M. Papas, F. Rousselle, and J. Novák. 2022. NeRF-
+Tex: Neural Reflectance Field Textures. Computer Graphics Forum 41, 6
+(March 2022), 287–301. https://doi.org/10.1111/cgf.14449
+
+W
+L.188R 0
+2021
+DW
+L1888809
+2021Fober, J.M.
+Wikipedia contributors. 2022. Fisheye lens: Mapping function. Wikipedia,
+The Free Encyclopedia.
+https://en.wikipedia.org/w/index.php?title=
+Fisheye_lens&oldid=1124809304#Mapping_function [Online].
+Alex Yu, Sara Fridovich-Keil, Matthew Tancik, Qinhong Chen, Benjamin
+Recht, and Angjoo Kanazawa. 2021. Plenoxels: Radiance Fields without
+Neural Networks. arXiv (Dec. 2021). https://doi.org/10.48550/ARXIV.
+2112.05131
+Received January 2023
+

B9AzT4oBgHgl3EQfwP5n/content/tmp_files/load_file.txt

@@ -0,0 +1,156 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf,len=155
+page_content='Radiance Textures for Rasterizing Ray-Traced Data  Jakub Maksymilian Fober  talk@maxfober.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='space  Abstract  Presenting real-time rendering of 3D surfaces using radiance  textures for fast synthesis of complex incidence-variable ef-  fects and environment interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' This includes iridescence,  parallax occlusion and interior mapping, (specular, regular,  diffuse, total-internal) reflections with many bounces, re-  fraction, subsurface scattering, transparency, and possibly  more.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' This method divides textures into a matrix of radiance  buckets, where each bucket represent some data at various  incidence angles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' Data can show final pixel color, or deferred  rendering ambient occlusion, reflections, shadow map, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  Resolution of the final synthesized output is the radiance  bucket matrix size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' Technique can be implemented with a  simple fragment shader.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' The computational footprint of this  technique is of simple diffuse-only graphics, but with vi-  sual fidelity of complex (off-line) ray-traced render at the  cost of storage memory footprint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' Balance between com-  putational footprint and storage memory footprint can be  easily achieved with variable compression ratio of repetitive  radiance scene textures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  CCS Concepts: • Computing methodologies → Reflectance  modeling;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' Rasterization;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' Texturing;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' Ray tracing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  Keywords: 3D graphics, holography, light field, plenoptic,  radiance field, rasterization, ray tracing, reflectance field  © 2023 Jakub Maksymilian Fober  This work is licensed under Creative Commons BY-NC-ND 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='0 license.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  https://creativecommons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='org/licenses/by-nc-nd/3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='0/  For all other uses including commercial, contact the owner/author(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  1  Introduction  Radiance and reflectance field rendering techniques are a  class of algorithms used in computer graphics to generate im-  ages of three-dimensional scenes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' These algorithms simulate  the way light interacts with surfaces in a virtual environment,  producing realistic and detailed images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  These techniques have been the subject of extensive re-  search in computer graphics and rendering, as they offer a  powerful and flexible way to generate high-quality images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  There is a wide range of applications for radiance and re-  flectance field algorithms, including film and video game  production, architectural visualization, and scientific visual-  ization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  In this paper, technique is presented to capture and render  complex precomputed light interactions, via radiance field  textures, embedded onto three-dimensional-object’s surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  The presented technique utilizes a standard fragment pixel  shader and a two-dimensional texture lookup to render dy-  namic, view-independent, photo-realistic images at a fraction  of the computational cost associated with effects such as real-  time ray tracing, parallax mapping, and dynamic shadowing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  It is well-suited for real-time execution in video games,  virtual reality, and virtual production environments on mod-  ern hardware.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' It can take advantage of the direct storage  capability in ninth-generation gaming systems, providing  high-fidelity, high-performance images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  This technique can replace computationally heavy rendering-  pipeline chains, while preserving hardware-accelerated, highly-  optimized rasterization elements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' It can also enable wider  implementation of real-time GPU ray-tracing, with ability  to combine bounce rays with precomputed radiance of the  environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='1  Previous work  Mainstream implementations of radiance field rendering  focus on volumetric data structures and spherical harmonics  for rendering images[Yu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' 2021].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' While volumetric data  can be sparse in order to exclude void regions[Yu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' 2021],  the ultimate goal would logically be to perfectly match the  geometry of the represented object.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' And since the inside  volume of the object is of no interest (most of the time), only  half of the radiance sphere is considered practically useful.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  Therefore, such fields could effectively be spread across the  surface of the object.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  Some researchers embraced this approach, with neural  reflectance fields as texturing primitives[Baatz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' 2022],  which rendered high-fidelity results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' But while neural fields  produce fantastic results, they are computationally inten-  sive at rendering time[Yu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' 2021] and therefore are not  suitable for real-time applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='2  Overview of the content  In this initial version of paper you will find theoretical ex-  planation and implementation of the subject, along with  equations and schematics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' Some elements had been tested,  like mapping functions, some yet to be presented, as the  follow-up updates continue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='3  Document naming convention  This document uses the following naming convention:  Left-handed coordinate system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='01719v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='GR]  4 Jan 2023  Fober, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  Vectors presented natively in column.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  Row-major order matrix arranged, denoted “𝑀row col”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  Matrix multiplication by “[column]𝑎 · [row]𝑏 = 𝑀𝑎 𝑏”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  A single bar enclosure “|𝑢|” represents scalar absolute.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  A single bar enclosure “|�𝑣|” represents vector’s length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  Vectors with an arithmetic sign, or without, are calcu-  lated component-wise and form another vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  Centered dot “·” represents the vector dot product.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  Square brackets with a comma “[𝑓 ,𝑐]” denote interval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  Square brackets with blanks “[𝑥 𝑦]” denote vectors  and matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  The power of “−1” implies the reciprocal of the value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  QED symbol “□” marks the final result or output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  This naming convention simplifies the process of transform-  ing formulas into shader code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  2  Methodology  Each pixel of the model’s texture contains discrete radiance  hemispherical map of size 𝑛 ×𝑛, called “bucket”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' Buckets are  arranged in place of initial texture’s pixels, increasing overall  resolution to 𝑤 ·𝑛 ×ℎ ·𝑛 pixels, where 𝑤 and ℎ denote width  and height of the synthesized output texture, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  Buckets are highly repetitive and change only slightly from  one to another.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' This is a great case for a simple compression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  To synthesize output texture for a given view position,  single sample per bucket is taken, giving normal resolution  texture output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  Model’s 𝑢, 𝑣 texture coordinates correspond to bucket ma-  trix position index, while incidence vector, correspond to  bucket’s internal 𝑢, 𝑣 position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' Therefore radiance texture  sampling algorithm can be described as a four-dimensional  plenoptic function 𝐿(𝑢, 𝑣,𝜃,𝜙), where 𝑢, 𝑣 denote model’s  texture coordinates and 𝜃,𝜙 incidence angles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' Radiance texture sampling model, where the inci-  dence R3 vector (blue) is projected and squarified (orange)  to R2 texture coordinates (red and green), which map onto  hemispherical radiance bucket represented as a flat square.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  Each radiance bucket should represent a hemisphere of  reflectivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' Equisolid azimuthal projection was chosen for  this task, for its properties, as it preserves area and resem-  bles spherical mirror reflection[Wikipedia contributors 2022].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  Resolution of the radiance bucket, in such projection, directly  corresponds to sin(𝜃/2)  √  2, where 𝜃 is the incidence angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  To efficiently spread information across square buckets, ad-  ditional disc-to-square mapping function was implemented,  providing uniform pixel count across both orthogonal direc-  tions and diagonal directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  Equisolid azimuthal projection mapping can be easily im-  plemented in the vector domain without the use of anti-  trigonometric functions, as the orthographically projected  normalized sum of the incidence and normal vectors has  a length of sin(𝜃/2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' This eliminates 𝜃,𝜙 angles from the  plenoptic function, resulting in new 𝐿′(𝑢, 𝑣,𝑥,𝑦,𝑧), where  𝑥,𝑦,𝑧 correspond to incidence unit-vector components in  orthogonal texture space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='1  Mapping of incident vector to radiance bucket  For every visible pixel there is an incidence vector ˆ𝐼 ∈ R3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  This vector can be mapped and projected to R2 texture coor-  dinates using translation and R2×3-matrix transformation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  Following equation maps incidence vector to azimuthal  equisolid projection, with 𝑟 = 1, at Ω = 180°.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  \uf8ee\uf8ef\uf8ef\uf8ef\uf8ef\uf8f0  �𝐴𝑥  �𝐴𝑦  √  2 cos 𝜃/2  \uf8f9\uf8fa\uf8fa\uf8fa\uf8fa\uf8fb  =  √  2  ������  \uf8ee\uf8ef\uf8ef\uf8ef\uf8ef\uf8f0  ˆ𝐼𝑥 + ˆ𝑁𝑥  ˆ𝐼𝑦 + ˆ𝑁𝑦  ˆ𝐼𝑧 + ˆ𝑁𝑧  \uf8f9\uf8fa\uf8fa\uf8fa\uf8fa\uf8fb  ������  (1a)  � �𝐴𝑥  �𝐴𝑦  �  =  √  2  ���ˆ𝐼𝑥  ˆ𝐼𝑦  ˆ𝐼𝑧 + 1  ���  �ˆ𝐼𝑥  ˆ𝐼𝑦  �  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' if ˆ𝑁𝑧 = 1  (1b)  Inverse mapping:  \uf8ee\uf8ef\uf8ef\uf8ef\uf8ef\uf8f0  ˆ𝐴′  𝑥  ˆ𝐴′  𝑦  ˆ𝐴′  𝑧  \uf8f9\uf8fa\uf8fa\uf8fa\uf8fa\uf8fb  =  \uf8ee\uf8ef\uf8ef\uf8ef\uf8ef\uf8ef\uf8f0  �𝐴𝑥  √︁  1/2  �𝐴𝑦  √︁  1/2  √︃  1 −  �𝐴2𝑥  2 −  �𝐴2𝑦  2  \uf8f9\uf8fa\uf8fa\uf8fa\uf8fa\uf8fa\uf8fb  (2a)  \uf8ee\uf8ef\uf8ef\uf8ef\uf8ef\uf8f0  ˆ𝐼𝑥  ˆ𝐼𝑦  ˆ𝐼𝑧  \uf8f9\uf8fa\uf8fa\uf8fa\uf8fa\uf8fb  = 2  ���  �  ˆ𝐴′ · ˆ𝑁  \uf8ee\uf8ef\uf8ef\uf8ef\uf8ef\uf8f0  ˆ𝐴′  𝑥  ˆ𝐴′  𝑦  ˆ𝐴′  𝑧  \uf8f9\uf8fa\uf8fa\uf8fa\uf8fa\uf8fb  −  \uf8ee\uf8ef\uf8ef\uf8ef\uf8ef\uf8f0  ˆ𝑁𝑥  ˆ𝑁𝑦  ˆ𝑁𝑧  \uf8f9\uf8fa\uf8fa\uf8fa\uf8fa\uf8fb  ���  �  +  \uf8ee\uf8ef\uf8ef\uf8ef\uf8ef\uf8f0  ˆ𝑁𝑥  ˆ𝑁𝑦  ˆ𝑁𝑧  \uf8f9\uf8fa\uf8fa\uf8fa\uf8fa\uf8fb  (2b)  =  \uf8ee\uf8ef\uf8ef\uf8ef\uf8ef\uf8ef\uf8ef\uf8f0  �𝐴𝑥  √︃  2 − �𝐴2𝑥 − �𝐴2𝑦  �𝐴𝑦  √︃  2 − �𝐴2𝑥 − �𝐴2𝑦  1 − �𝐴2  𝑥 − �𝐴2  𝑦  \uf8f9\uf8fa\uf8fa\uf8fa\uf8fa\uf8fa\uf8fa\uf8fb  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' if ˆ𝑁𝑧 = 1  (2c)  where �𝐴 ∈ [−1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' 1]2 is the azimuthal equisolid projection  coordinate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' 𝜃 is the incidence angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' ˆ𝑁 ∈ R3 is the surface  normal vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' As the incidence ˆ𝐼 ∈ R3 is mapped to or from  orthogonal texture space, where ˆ𝑁𝑧 = 1, the transformation  can take form of equation 1b and 2c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  Radiance Textures for Rasterizing Ray-Traced Data  Following equation transforms azimuthal projection vec-  tor, into square coordinates, for the radiance bucket sam-  pling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='1  � �𝐵𝑥  �𝐵𝑦  �  =  �� � �𝐴𝑥  �𝐴𝑦  � ��  max �| �𝐴𝑥 |, | �𝐴𝑦|�  � �𝐴𝑥  �𝐴𝑦  �  if �𝐴𝑥 and �𝐴𝑦 ≠ 0  (3)  where �𝐵 ∈ [−1, 1]2 is the bucket’s centered texture coordi-  nate and �𝐴 ∈ [−1, 1]2 is the azimuthal projection vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  Note.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' It is important to prevent pixel blending between  edges of neighboring buckets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' This can be done by clamping  bucket coordinates to �𝐵 ∈ [𝐵−1  res − 1, 1 − 𝐵−1  res]2 range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  Inverse transformation of bucked, centered coordinates  �𝐵 ∈ R2 to azimuthal projection coordinates ˆ𝐴 ∈ R2 can be  achieved with same, but inverted method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  � �𝐴𝑥  �𝐴𝑦  �  = max �| �𝐵𝑥 |, | �𝐵𝑦|�  √︃  �𝐵2𝑥 + �𝐵2𝑦  � �𝐵𝑥  �𝐵𝑦  �  (4a)  \uf8ee\uf8ef\uf8ef\uf8ef\uf8ef\uf8f0  ˆ𝑅𝑥  ˆ𝑅𝑦  ˆ𝑅𝑧  \uf8f9\uf8fa\uf8fa\uf8fa\uf8fa\uf8fb  =  \uf8ee\uf8ef\uf8ef\uf8ef\uf8ef\uf8ef\uf8ef\uf8f0  − �𝐴𝑥  √︃  2 − �𝐴2𝑥 − �𝐴2𝑦  − �𝐴𝑦  √︃  2 − �𝐴2𝑥 − �𝐴2𝑦  1 − �𝐴2  𝑥 − �𝐴2  𝑦  \uf8f9\uf8fa\uf8fa\uf8fa\uf8fa\uf8fa\uf8fa\uf8fb  (4b)  where ˆ𝑅 ∈ R3 denotes equisolid reflection vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' This vector  is used to sample ray-traced data onto radiance field texture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  It is a version of the vector mirrored along the normal, found  in equation 2c on the preceding page.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  3  Results  TBA  4  Conclusion  I have theorized about possible implementation of radiance  field texturing using modern hardware shading capabilities,  and presented mathematical solution for executing such con-  cept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  Note.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' More conclusion are to be added, after the update to  the paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  5  Possible applications  Radiance field texture sampling can replace shading pipeline  or supplement it with enhanced effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' Some such effects  include:  Parallax interior mapping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' This effect is used to mimic  interior of a room, as seen through a window, or it can simu-  late a portal to another place.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  Proxy meshes with parallax mapping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' Radiance tex-  ture with alpha mask can simulate more complex or furry  objects bound inside a proxy mesh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' Similarly to neural radi-  ance fields texturing primitives[Baatz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' 2022].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  1See figure 2 for visual reference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  (a) Picture of one cent American coin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  (b) One cent coin mapped to a rectangle, using equation 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' A visual example of disc to square mapping using  the formulation found in equation 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  Reflections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' Many light bounces can be combined into a  single pixel of the radiance texture map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' Dynamic objects  can then sample such radiance field to obtain environment  reflections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' Also semi real-time ray-tracing can accumulate  dynamically generated reflections into such texture map, to  update and enhance environment one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  Shadowing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' 1-bit radiance field texture map can repre-  sent shadowing of static objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' Here, incidence vector is  replaced with light direction vector for shadow occlusion  sampling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' It can work with both parallel light sources and  point lights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' With more than one sample per bucket, area  shadows are possible to produce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  Subsurface scattering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' This computationally demand-  ing effect can be encoded in a radiance texture map, which  then replaces incidence vector, with the light direction vector  in relation to the view position for sampling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  References  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' Baatz, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' Granskog, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' Papas, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' Rousselle, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' Novák.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' NeRF-  Tex: Neural Reflectance Field Textures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' Computer Graphics Forum 41, 6  (March 2022), 287–301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='1111/cgf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='14449  W  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='188R 0  2021  DW  L1888809  2021Fober, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  Wikipedia contributors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' Fisheye lens: Mapping function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' Wikipedia,  The Free Encyclopedia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  https://en.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='wikipedia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='org/w/index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='php?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='title=  Fisheye_lens&oldid=1124809304#Mapping_function [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  Alex Yu, Sara Fridovich-Keil, Matthew Tancik, Qinhong Chen, Benjamin  Recht, and Angjoo Kanazawa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' Plenoxels: Radiance Fields without  Neural Networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' arXiv (Dec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='48550/ARXIV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='  2112.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}
+page_content='05131  Received January 2023' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9AzT4oBgHgl3EQfwP5n/content/2301.01719v1.pdf'}

B9FJT4oBgHgl3EQfACzo/content/tmp_files/2301.11418v1.pdf.txt

@@ -0,0 +1,980 @@
+Parkinson gait modelling from an anomaly deep
+representation
+Edgar Rangela, Fabio Martineza,∗
+a Biomedical Imaging, Vision and Learning Laboratory (BIVL2ab), Universidad Industrial
+de Santander, 680002, Bucaramanga, Colombia
+Abstract
+Parkinson’s Disease is associated with gait movement disorders, such as pos-
+tural instability, stiffness, and tremors. Today, some approaches implemented
+learning representations to quantify kinematic patterns during locomotion, sup-
+porting clinical procedures such as diagnosis and treatment planning. These
+approaches assumes a large amount of stratified and labeled data to optimize
+discriminative representations. Nonetheless, these considerations may restrict
+the operability of approaches in real scenarios during clinical practice.
+This
+work introduces a self-supervised generative representation, under the pretext
+of video reconstruction and anomaly detection framework. This architecture
+is trained following a one-class weakly supervised learning to avoid inter-class
+variance and approach the multiple relationships that represent locomotion. For
+validation 14 PD patients and 23 control subjects were recorded, and trained
+with the control population only, achieving an AUC of 86.9%, homoscedasticity
+level of 80% and shapeness level of 70% in the classification task considering its
+generalization.
+Keywords:
+Anomaly detection, Deep Learning, Weakly Supervised, Parkinson
+Disease
+1. Introduction
+Parkinson’s Disease (PD) is the second most common neurodegenerative dis-
+order, affecting more than 6.2 million people worldwide [1, 2]. According to the
+World Health Organization, this number will increase by more than 12 million by
+2030 [3]. PD is characterized by the progressive loss of dopamine, a neurotrans-
+mitter involved in the execution of voluntary movements. For this reason, the
+main diagnostic support is based on the observation and analysis of progressive
+motor disorders, such as tremor, rigidity, slowness of movement (bradykinesia),
+∗Corresponding author
+Email addresses: [email protected] (Edgar Rangel),
+[email protected] (Fabio Martinez)
+URL: https://bivl2ab.uis.edu.co/ (Fabio Martinez)
+Preprint submitted to Pattern Recognition
+January 30, 2023
+arXiv:2301.11418v1  [cs.CV]  26 Jan 2023
+
+postural instability, among many other related symptoms [4]. Despite of impor-
+tant advances to determine the sources of the disease and multiple symptoms,
+today, there is not a definitive and universal biomarker to characterize, diagnose,
+and follow the patient progression of PD patients.
+Particularly, the gait is a multi-factorial and complex locomotion process
+that involves several subsystems. The associated kinematics patterns are typ-
+ically recovered over standard marker-based setups, that coarsely approximate
+complex motion behaviors, resulting in restrictive, intrusive and, altering natu-
+ral postural gestures for PD description. Alternative, markerless video strate-
+gies together with discriminative learning approximations have emerged as key
+solutions to support the PD characterization and classification from other dis-
+eases [5–9]. These methodologies have been successful in controlled studies but
+strongly require a stratified, balanced, and well-labeled dataset to avoid over-
+fitting. Besides, these approaches are biased to the physicians’ experience to
+determine the disease and limiting the quantification to general scale indexes
+[10]. Even worst, these approaches solve classification tasks but remains limited
+on further explanation about data representation to define the generalization
+capability w.r.t the new data.
+This work introduces a deep generative and anomaly architecture to learn a
+hidden descriptor to represent locomotion patterns. Following a weakly super-
+vised methodology, a 3D net is self-trained under a gait video reconstruction pre-
+text. Then, the resultant embedding representation encodes complex dynamic
+gait relationships, captured from control population, that allows to discrimi-
+nate parkinson patients. The main contributions of this work are summarized
+as follows:
+• A new digital biomarker coded as an embedding vector with the capability
+to represent hidden kinematic relationships of Parkinson disease.
+• A 3D Convolutional GAN net dedicated to learn spatio-temporal pat-
+terns of gait video-sequences. This architecture integrates an auto-encoder
+net to learn video patterns in reconstruction tasks and a complementary
+decoder that discriminates between reconstructed and original video se-
+quences.
+• A statistical test framework to validate the capability of the approach in
+terms of generalization, coverage of data and discrimination capability for
+any class with different groups between them, i.e. evaluate the general-
+ization of Parkinsonian patients, at different stages of the disease, with
+respect to a control population.
+2. Current Work
+Deep discriminative learning is nowadays the standard methodology in much
+of the computer vision challenges, demonstrating remarkable results in very dif-
+ferent domains. For instance, the Parkinson characterization is achieved from
+2
+
+sensor-based and vision-based approaches, following a supervised scheme to cap-
+ture main observed relationships and to generate a particular prediction about
+the condition of the patients [5]. These approaches in general are dedicated
+to classify and discriminate between a control population and patients with the
+Parkinson condition. The sensor-based approaches capture kinematics from mo-
+tion signals, approximating to PD classification, but in many of the cases results
+marker-invasive, alter natural gestures, and only have recognition capabilities
+in advanced stages of the disease [11]. Contrary, the vision-based approaches
+exploit postural and dynamic features, from video recordings, but the represen-
+tations underlies on supervised schemes that requires a large amount of labeled
+data to learn the inter and intra variability among classes [6–9]. Also, these
+learning methodologies require that training data have well-balanced conditions
+among classes, i.e., to have the same proportion of sample observations for each
+of the considered class [12].
+Unsupervised, semi-supervised and weakly supervised approaches have emerged
+as a key alternative to model biomedical problems, with significative variabil-
+ity among observations but limited training samples.
+However, to the best
+of our knowledge, these learning methods have been poorly explored and ex-
+ploited in Parkinson characterization, with some preliminary alternatives that
+use principles of Minimum Distance Classifiers and K-means Clustering [5, 13–
+17]. In such sense, the PD modelling from non-supervised perspective may be
+addressed from reconstruction, prediction and generative tasks [18], that help
+to determine sample distributions and determine future postural and kinematic
+events. In fact, the PD pattern distribution results key to understand multi-
+factorial nature of PD, being determinant to define variations such as laterality
+affectation of disease, abnormality sources, but also to define patient prognosis,
+emulating the development of a particular patient during the gait.
+3. Proposed approach
+This work introduces a digital PD biomarker that embedded gait motor pat-
+terns, from anomaly video reconstruction task. Contrary to typical classification
+modeling, we are dedicated to deal with one class learning, i.e., only to learn
+control gait patterns, approaching the high variability on training samples, with-
+out using explicit disease labels. Hence, we hypothesize that a digital biomarker
+of the disease can be modeled as a mixture of distributions, composed of samples
+that were labeled as outliers, from learned representation. In consequence, we
+analyze the embedding, reconstruction, and discrimination space to later define
+rules to separate Parkinson from control vectors, during test validation. The
+general pipeline of the proposed approach is illustrated in Figure 1.
+3.1. A volumetric autoencoder to recover gait embedding patterns
+Here, we are interested on capture complex dynamic interactions during lo-
+comotion, observed in videos as spatio-temporal textural interactions. From a
+self-supervised strategy (video-reconstruction task), we implemented a 3D deep
+3
+
+Figure 1: Pipeline of the proposed model separated in volumetric auto-encoder to recover gait
+patterns (a), Digital gait biomarker (b), Auxiliary task to discriminate reconstructions (c),
+and statistical validation of learned classes distributions (d)
+autoencoder that projects videos into low-dimensional vectors, learning the com-
+plex gait dynamics into a latent space (see the architecture in Figure 1-a). For
+doing so, 3D convolutional blocks were implemented, structured hierarchically,
+with the main purpose to carry out a spatio-temporal reduction while increasing
+feature descriptions. Formally, a gait sequence x ∈ Nf×h×w×c, where f denotes
+the number of temporal frames, (h × w) are the spatial dimensions, and c is the
+number of color channels in the video. This sequence is received as input in the
+convolutional block which is convolved with a kernel κ of dimensions (kt, kh,
+kw), where kt convolves on the temporal axis and kh, kw on the spatial axes.
+At each level l of processing, we obtain a new volume xl ∈ Zf/2l×h/2l×w/2l×2lc
+that represents a bank of spatio-temporal feature maps. Each of these volumet-
+ric features are dedicated to stand out relevant gait patterns in a zG reduced
+projection, that summarizes a multiscale gait motion representation.
+The resultant embedding vector zG encodes principal dynamic non-linear
+correlations, which are necessary to achieve a video reconstruction x′. In this
+study, the validated datasets are recorded from a relative static background, so,
+the major dependencies to achieve an effective reconstruction lies in temporal
+and dynamic information expressed during the gait. Here, we adopt zG as a
+digital gait biomarker that, among others, allows to study motion abnormalities
+associated to the Parkinson disease.
+To complete end-to-end learning, 3D transposed convolutional blocks were
+implemented as decoder, positioned in a symmetrical configuration regarding the
+encoder levels, and upsampling spatio-temporal dimensions to recover original
+video-sequence. Formally, having the embedded feature vector zG ∈ Zn with
+n coded features, we obtain x′l ∈ Z2lf×2lh×2lw×c/2l volumes from transpose
+4
+
+Generator
+Conv 3D
+Conv 3D
+Conv 3D
+ZG
+Decoder
+Encoder
+2'G
+Encoder
+a
+(a)
+(b)
+Discriminator
+Statistical Validation
+Xtest
+control
+-test
+control
+control?
+Conv 3D
+Encoder
+ZD
+Dense
+Xtest
+parkinson
+(c)
+(d)convolutional blocks until obtaining a video reconstruction x′ ∈ Nf×h×w×c. The
+quality of reconstruction is key to guarantee the deep representation learning
+in the autoencoder part of generator. To do this, an L1 loss is implemented
+between x and x′ and its named contextual loss: Lcon = ∥x − x′∥1.
+3.2. Auxiliary task to discriminate reconstructions
+From a generative learning, the capability of the deep representations to code
+locomotion patterns may be expressed in the quality of video reconstructions
+x′. Hence, we hypothesize that embedding descriptors zG that properly repro-
+duce videos x′ should encode sufficient kinematic information of trained class,
+allowing to discriminate among locomotion populations, i.e. between control
+and Parkinson samples.
+To measure this reconstruction capability, an auxiliary task is here intro-
+duced to receive tuples with original and reconstructed videos (x, x′), and out-
+put a discriminatory decision y = {y, y′}, regarding video source.
+In such
+case, y corresponds to the label for real videos, while y′ as labels for embed-
+dings from reconstructed sequences. For doing so, we implement an adversarial
+L2 loss, expressed as: Ladv = ∥zD − z′
+D∥2. In such case, for large differences
+between (zD, z′
+D) it will be a significant error that will be propagated to the
+generator. It should be noted that such minimization rule optimizes only the
+generator. Then discriminator is only minimized following a classical equally
+weighted cross-entropy rule, as: Ldisc = log(y)+log(1−y′)
+2
+.
+The auxiliary task to monitor video reconstruction is implemented from a
+discriminatory convolutional net that follows the same structure that encoder
+in Figure 1-a, which halves the spatio-temporal dimension while increases the
+features and finally dense layer determines its realness level (see in Figure 1-
+c.). Interestingly, from such deep convolutional representation the input videos
+are projected to an embedding vector zD ∈ Zm with m coded features, which
+thereafter may be used as latent vectors descriptors that also encode motion
+and realness information. To guarantee an optimal coding into low-dimensional
+embeddings, the reconstructed video x′ is mapped to an additional encoder
+projecting representation basis in a z′G embedding. In such sense, zG and z′G
+must be similar, and lead to x and x′ to be equal which helps in generalization
+of the generator, following an encoder L2 loss: Lenc = ∥zG − z′
+G∥2.
+3.3. A Digital gait biomarker from anomaly embeddings
+The video samples are high-dimensional motor observations that can be
+projected into a low-dimensional embedding space, through the proposed model.
+Formally, each video sample is an independent and random variable x(i)
+ℓ
+from the
+class (i) that follows a distribution x(i)
+ℓ
+∈ Ψ(i)[µ(x(i)), σ(x(i))] with mean µ(x(i)),
+and standard deviation σ(x(i)). We then considered the proposed model as an
+operator that transform each sample F(x(i)
+ℓ ) into a low dimensional space, while
+preserves the original distribution, as: F(x(i)
+ℓ ) ∈ Ψ(i)[F(µ(x(i))), F(σ(x(i)))].
+From this assumption we can measure statistical properties over low-dimensional
+space and explore properties as the generalization of the modeling.
+5
+
+Figure 2: Field of action of standard metrics of the model, where the dataset used only cover
+the intersection area but the model performance for new samples is not being evaluated
+Hence, we can adopt a new digital kinematic descriptor by considering em-
+bedding vector differences between (zG, z′G). For instance, large difference be-
+tween zG, z′G may suggest a new motion class, regarding the original distribu-
+tion of training. From such approximation, we can model a scheme of one-class
+learning (in this case, anomaly learning) over the video distributions from the
+low-embedding differences observations. This scheme learns data distribution
+without any label constraint. Furthermore, if we train the architecture only with
+videos of a control population (c), we can define a discriminatory problem from
+the reconstruction, by inducing: ∥zG − z′G∥2 ≤ τ → c ∧ ∥zG − z′G∥2 > τ → p,
+where p is a label imposed to a video with a significant error reconstruction and
+projected to a Parkinson population.
+3.4. Statistical validation setup
+This new discriminatory descriptor can be validated following standard met-
+rics into binary projection ˆy = {c, p}. For a particular threshold τ we can re-
+cover metrics such as the accuracy, precision and recall. Also, ROC-AUC (the
+Area Under the Curve) can estimate a performance by iterating over different
+τ values. However, these metrics say us about the capability of the proposed
+approach to discriminate classes but not about data distribution among classes
+[19, 20]. To robustly characterize a Parkinson digital biomarker is then demand-
+ing to explore more robust statistical alternatives that evidence the generaliza-
+tion of the embedded descriptor and estimate the performance for new samples
+(Figure 2 illustrates typical limitations of standard classification metrics for un-
+seen data being positioned on unknown places). In fact, we hypothesize that
+Parkinson and control distributions, observed from an embedding representa-
+tion, should remain with equal properties from training and test samples. To
+address such assumption, in this work is explored two statistical properties to
+validate the shape and variance of motor population distributions:
+6
+
+Ctest
+Ctest
+parkinson
+Conv 3D
+Encoder3.4.1. Variance analysis from Homoscedasticity
+Here, a equality among variance of data distributions is estimated through
+homoscedasticity operators. Particularly, this analysis is carried out for two
+independent groups ⟨k⟩, ⟨u⟩ with cardinality |x(i)
+⟨k⟩|, |x(j)
+⟨u⟩| of classes (i), (j). Here,
+it was considered two dispersion metrics regarding the Levene mean (∆⟨g⟩
+ℓ
+=
+|x⟨g⟩
+ℓ
+− µ(x⟨g⟩)|), and the Brown-Forsythe median (∆⟨g⟩
+ℓ
+= |x⟨g⟩
+ℓ
+− med(x⟨g⟩)|).
+From such dispersion distances, the test statistic W between x(i)
+⟨k⟩ and x(j)
+⟨u⟩ can
+be defined as:
+W = N − |P|
+|P| − 1
+�
+g∈P [|x⟨g⟩|(µ(∆⟨g⟩) − µ(∆))2]
+�
+g∈P [�
+ℓ∈x⟨g⟩ (∆⟨g⟩
+ℓ
+− µ(∆⟨g⟩))2]
+(1)
+where P = {x(i)
+⟨k⟩, x(j)
+⟨u⟩, · · · } is the union set of every data group from all
+classes, |P| is the cardinality of P, N is the sum of all |x⟨g⟩| cardinalities, µ(∆⟨g⟩)
+correspond to the mean ⟨g⟩ of ∆⟨g⟩
+ℓ
+values and µ(∆) is the overall mean of every
+∆⟨g⟩
+ℓ
+value in P. This estimation evaluates if the samples between two different
+groups are equally in variance for the same class, leading us to the first step in
+model generalization for any new sample related to trained data. Additionally,
+the homoscedasticity property is useful when is needed to check if two groups
+remains in the same distribution range, because two distribution can have the
+same shape (frequency) but be placed at different domain range, indicating a
+weakness for the model in new data domains.
+From a statistical test perspective, the value W rejects the null hypothesis
+of homocedasticity when W > fα,|P|−1,N−|P| where fα,|P|−1,N−|P| is the upper
+critical value of Fischer distribution with |P|−1 and N −|P| degrees of freedom
+at a significance level of α (generally 5%). This metric allows to estimate the
+clustering level for the model and determine if new data samples from another
+domain are contained in data distributions of control or Parkinson patients.
+Then, the homoscedasticity value of x(i)
+⟨k⟩ against x(j)
+⟨u⟩ is defined as follow:
+H(x(i)
+⟨k⟩, x(j)
+⟨u⟩) =
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+W(µ(x(i)
+⟨k⟩, x(j)
+⟨u⟩)) + W(med(x(i)
+⟨k⟩, x(j)
+⟨u⟩))
+2
+i = j ∧ k ̸= u
+0
+i = j ∧ k = u
+2 − (W(µ(x(i)
+⟨k⟩, x(j)
+⟨u⟩)) + W(med(x(i)
+⟨k⟩, x(j)
+⟨u⟩)))
+2
+i ̸= j
+(2)
+3.4.2. Shapeness analysis from ChiSquare
+Here, we quantify the “shapenes” focused in having equally distributions.
+Following the ChiSquare test χ2 between x(i)
+⟨k⟩ and x(j)
+⟨u⟩ as:
+7
+
+χ2 =
+�
+ℓ
+(x⟨k⟩
+ℓ
+− x⟨u⟩
+ℓ
+)2
+x⟨u⟩
+ℓ
+(3)
+From this rule, it should be considered that both groups must have the
+same cardinality (|x⟨k⟩| = |x⟨u⟩|) and the respective data sorting determines
+the direction of comparison (i.e. the direction goes from group ⟨k⟩ to have the
+same distribution of ⟨u⟩). To address these issues we make that the lower group
+will be repeated in its elements without adding new unknown data to preserve
+its mean and standard deviation, and secondly, we evaluate both directions to
+quantify the similarity when χ2(x(i)
+⟨k⟩ → x(j)
+⟨u⟩) and χ2(x(j)
+⟨u⟩ → x(i)
+⟨k⟩).
+The value χ2 reject the null hypothesis of equal distributions when χ2 >
+χ2
+α,|x⟨g⟩|−1 where χ2
+α,|x⟨g⟩|−1 is the upper critical value of Chi Square distribution
+with |x⟨g⟩| − 1 degrees of freedom at a significance level of α. We define the
+shapeness value as:
+Sh(x(i)
+⟨k⟩, x(j)
+⟨u⟩) =
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+χ2(x(i)
+⟨k�� → x(j)
+⟨u⟩) + χ2(x(j)
+⟨u⟩ → x(i)
+⟨k⟩)
+2
+i = j ∧ k ̸= u
+0
+i = j ∧ k = u
+2 − (χ2(x(i)
+⟨k⟩ → x(j)
+⟨u⟩) + χ2(x(j)
+⟨u⟩ → x(i)
+⟨k⟩))
+2
+i ̸= j
+(4)
+This test can be used directly as indicator of how relatively far are the
+samples from each other.
+Hence, a higher value of this metric means that
+the samples will be clearly different and separated, but there is the possibility
+that control patients’ distribution is near to parkinson’s while parkinson can be
+clearly far. Finally, in algorithm 1 is showed the steps to calculate the proposed
+homoscedasticity and shapeness level for the model.
+4. Experimental setup
+4.1. Datasets
+In this study were recruited 37 patients from control (23 subjects with av-
+erage age of 64.7 ± 13 ) and parkinson (14 subjects with an average age of
+72.8 ± 6.8) populations. The patients were invited to walk (without any mark-
+ers protocol), developing a natural locomotion gesture. Parkinson participants
+were evaluated by a physiotherapist (with more than five years of experience)
+and stratified according to the H&Y scale (level 1.0 = 2, level 1.5 = 1, level
+2.5 = 5, and level 3.0 = 6 participants). These patients written an informed
+consent and the total dataset count with the approval of the Ethics Committee
+of Universidad Industrial de Santander.
+For recording, during a natural walking in around 3 meters, the locomotion
+was registered 8 times from a sagittal view, following a semi-controlled condi-
+tions (a green background). In this study we use a conventional optical camera
+8
+
+Algorithm 1 Calculation of homoscedasticity and shapeness metric for any
+quantity of data groups with any classes
+Require: C = {c0, c1, · · · , cn}
+▷ Classes in dataset
+Require: Gci =
+�
+x(i)
+⟨0⟩, x(i)
+⟨1⟩, · · · , x(i)
+⟨mi⟩
+�
+∀ci ∈ C
+▷ Partitions per classes
+h ← 0
+s ← 0
+for any pair (ci, cj) in C do
+for any pair (x(i)
+⟨k⟩, x(j)
+⟨u⟩) in �(Gci, Gcj) do
+h ← h + H(x(i)
+⟨k⟩, x(j)
+⟨u⟩)
+▷ H defined in eq. 2
+s ← s + Sh(x(i)
+⟨k⟩, x(j)
+⟨u⟩)
+▷ Sh defined in eq. 4
+end for
+end for
+N ← �n
+i |Gci|
+d ←
+�N
+2
+�
+▷ Combinatory of N in groups of 2
+h ← h
+d
+▷ Homocedasticity level metric
+s ← s
+d
+▷ Shapeness level metric
+Nikon D3500, that output sequences at 60 fps with a spatial resolution of 1080p.
+The camera was localized to cover the whole participant silhouette. Every se-
+quence was spatially resized to 64×64 pixels, and temporally cropped to 64
+frames. Besides, the videos were normalized and a subsequent subsampling was
+carried out to ensure a complete gait cycle. To follow one learning class, the
+proposed approach was trained only with control subjects. In such case, the set
+of control patients was split in common train, validation and test partitions of
+11, 3 and 9 randomly patients selected, respectively. For parkinson participants,
+we take for validation and test partitions of 3 and 11 patients randomly selected
+to complement validation and test control sets. Hence, we balanced data for
+standard and statistical validation purposes.
+4.1.1. External dataset validation
+A main interest in this work is to measure the capability to generalize motion
+patterns from anomaly deep representations. Also, we are interested in mea-
+suring the capability of embedding descriptors to discriminate PD from other
+classes, even for videos captured with external protocols. Hence, in this work
+we only evaluate the proposed approach with a public dataset of walking videos
+that include knee-osteoarthritis (50 subjects with an average age of 56.7 ± 12.7),
+parkinson (16 subjects with an average age of 68.6 ± 8.3) and control (30 sub-
+jects with an average age of 43.7 ± 9.3) patients [21]. The 96 participants were
+recorded with a static green background, blurred faces and markers on their
+bodies. Following the same methodology for owner data, each sequence was
+spatially resized to 64×64 pixels, and temporally cropped to 64 frames, and
+finally normalized and subsampled ensuring a complete gait cycle.
+9
+
+4.2. Model configuration
+The introduced strategy has in the generator an autoencoder and encoder
+net, while the discriminator has an encoder net. The encoders use three layers
+that include 3D (4×4×4 and stride 2×2×2) convolutions, BatchNormalization
+(momentum of 0.1 and epsilon of 1 × 10−5) and LeakyRelu (α = 0.2).
+At
+each progressive level, the input is reduced to half in spatial and temporal
+dimensions while the features are increased twice. The decoder network follows
+a symmetrical configuration against the encoder with same layers as encoder
+(replacing 3D convolutions by 3D transpose convolutions). The overall structure
+is summarized in table 1.
+Table 1: Generator and Discriminator Networks structure summary
+Module
+Network
+Levels
+Input
+Output
+Generator
+Encoder
+5
+64×64×64×1
+1×1×1×n
+Decoder
+5
+1×1×1×n
+64×64×64×1
+Discriminator
+Encoder
+5
+64×64×64×1
+1×1×1×1
+5. Evaluations and Results
+The proposed strategy was exhaustively validated with respect to the ca-
+pability to recognize parkinsonian inputs as abnormal class patterns in archi-
+tectures trained only with control patterns and under challenging unbalanced
+and scarce scenarios. Hence, in the first experiment, the proposed strategy was
+trained only with control samples from owner dataset, following a video recon-
+struction pretext task. Hence, encoder (∥zG − z′
+G∥2), contextual (∥x − x′∥1)
+and adversarial (∥zD − z′
+D∥2) embedding errors were recovered as locomotor
+descriptors of the observed sequences. For classification purposes, these errors
+were binarized by imposing a threshold value, as: τzG = 1.768 for encoder,
+τx = 0.147 for contextual, and τzD = 0.429 for adversarial errors. Table 2 sum-
+marizes the achieved performance of three locomotor descriptors according to
+standard classification metrics. In general, the proposed strategy reports a re-
+markable capability to label parkinson patterns as abnormal samples, which are
+excluded from trained representation. Interestingly, the contextual errors have
+the highest value among the others to classify between control and parkinson
+patients, reporting a remarkable 86.9% in AUC, with mistakes in only 64 video
+clips (approximately 3 patients).
+For robustness validation, we are also interested in the distribution out-
+put of predictions, which may suggest the capability of generalization of the
+model. For doing so, we also validate locomotion descriptors with respect to
+10
+
+Table 2: Model performance for encoder, contextual and adversarial losses using standard
+metrics when the model trains with control patients. Acc, Pre, Rec, Spe, F1 are for accuracy,
+precision, recall, specificity and f1 score respectively.
+Loss
+Acc
+Pre
+Rec
+Spe
+F1
+ROC-AUC
+Encoder
+53.8%
+89.5%
+20.4%
+96.9%
+33.2%
+58.7%
+Contextual
+85.7%
+96.6%
+77.4%
+96.4%
+85.7%
+86.9%
+Adversarial
+75.5%
+94.3%
+60%
+95.4%
+73.3%
+77.7%
+introduced homoscedasticity and shapeness validation. Table 3 summarizes the
+results achieved by each locomotion embedding descriptor, contrasting with the
+reported results from standard metrics. In such case, the validated metrics sug-
+gest that contextual errors may be overfitted for the trained dataset and the
+recording conditions, which may be restrictive for generalized architecture in
+other datasets. Contrary, the encoder descriptor shows evident statistical ro-
+bustness from variance and shapeness distributions. Furthermore, the encoder
+losses evidence a clearly separation between the control and parkinson distribu-
+tion in Figure 3, where even the proposed model can separate stages of Hoehn
+& Yahr with the difference between 2.5 and 3.0 levels where the ChiSquare test
+shows us that both distributions remains equals meaning that both stages are
+difficult to model.
+Table 3: Model performance for encoder, contextual and adversarial losses using the proposed
+statistical metrics when the model trains with control patients.
+Loss
+Homocedasticity
+Shapeness
+Encoder
+80%
+70%
+Contextual
+50%
+40%
+Adversarial
+50%
+45%
+To follow with one of the main interests in this work i.e, the generaliza-
+tion capability, the proposed strategy was validated with an external public
+dataset (without any extra training) that include parkinson (16 patients), knee-
+osteoarthritis (50 patients) and control patients (30 patients) [21]. Table 4 sum-
+marized the achieved results to discriminate among the three unseen classes,
+evidencing a notable performance following encoder embedding representation.
+It should be noted, that Encoder achieves the highest ROC-AUC, reporting an
+average of 75%, being the more robust representation, as suggested by statistical
+11
+
+Figure 3: Data distribution given by the proposed model for control and parkinson samples
+by Hoehn & Yahr levels.
+homoscedasticity and shapeness validation. The contextual and the adversarial
+losses have better accuracy, precision and recall, but the specificity suggests
+that there is not any evidence of correctly classifying control subjects. In such
+sense, the model label all samples as abnormal from trained representation.
+In contrast, the encoder element in the network (Figure 1-a) capture relevant
+gait patterns to distinguish between control, parkinson and knee-osteoarthritis
+patients.
+Table 4: Model performance for encoder, contextual and adversarial losses using the proposed
+model without retraining and same thresholds as Table 2. Acc, Pre, Rec, Spe, F1 are for
+accuracy, precision, recall, specificity and f1 score respectively.
+Loss
+Acc
+Pre
+Rec
+Spe
+F1
+ROC-AUC
+Encoder
+62.6%
+97.9%
+58.1%
+91.9%
+72.9%
+75%
+Contextual
+86.7%
+86.7%
+100%
+0%
+92.9%
+50%
+Adversarial
+87.8%
+89.4%
+97.4%
+24.9%
+93.3%
+61.2%
+Along the same line, the external dataset was also validated with respect
+to homoscedasticity and shapeness metrics. Table 5 summarizes the achieved
+results from the distribution representation of output probabilities. As expected,
+the results enforce the fact that embeddings from the Encoder have much better
+generalization against the other losses, allowing to discriminate among three
+different unseen classes. Remarkably, the results suggest that control subjects
+of the external dataset belong to the trained control set. This fact is relevant
+because indicates that architecture is principally dedicated to coded locomotor
+patterns without strict restrictions about captured conditions. To complement
+such results, output probabilities from three classes are summarized in violin
+plots, as illustrated in Figure 4 which shows the separation between the classes
+of parkinson and knee-osteoarthritis, also, between levels of the diseases, being
+remarkable the locomotor affectations produced by the patients diagnosed with
+knee-Osteoarthritis.
+12
+
+25 
+20 
+p< 0.05
+p< 0.05
+15
+Encoder Errors
+p<0.05
+p< 0.05
+10
+p<0.05
+p> 0.05
+Y
+5
+0
+0 
+-5
+-10
+Control
+Stage 1.0
+Stage 1.5
+Stage 2.5
+Stage 3.0Table 5: Model performance for encoder, contextual and adversarial losses using the proposed
+statistical metrics and model as Table 2.
+Loss
+Homocedasticity
+Shapeness
+Encoder
+66.7%
+66.7%
+Contextual
+83.4%
+0%
+Adversarial
+16.7%
+16.7%
+Figure 4: Data distribution given by the proposed model for control, parkinson (PD) and
+knee-osteoarthritis (KOA) samples by levels where EL is early, MD medium and SV severe.
+Alternatively, in an additional experiment we train using only patients di-
+agnosed with parkinson to force the architecture to extract these abnormal
+locomotion patterns. In such cases, the videos from control subjects are associ-
+ated with abnormal responses from trained architecture. Table 6 summarizes the
+achieved results from standard and statistical distribution metrics. As expected,
+from this configuration of the architecture is achieved a lower classification per-
+formance because the high variability and complexity to code the disease. In
+fact, parkinson patients may manifest totally different locomotion affectations
+at the same stage. For such reason, the architecture has major challenges to
+discriminate control subjects and therefore lower agreement with ground truth
+labels. The statistical homoscedasticity and shapeness metrics confirm such is-
+sue achieving scores lower than 50% and indicating that the model, from such
+configuration, is not generalizable. In this configuration, it would be demanding
+a larger amount of parkinson patients to deal with disease variability.
+6. Discussion
+This work presented a deep generative scheme, designed under the one-class-
+learning methodology to model gait locomotion patterns in markerless video
+sequences. The proposed architecture is trained under the reconstruction video
+pretext task, being categorical to capture kinematic behaviors without the asso-
+13
+
+15.0
+p< 0.05
+p> 0.05
+T
+12.5
+p<0.05
+p<0.05
+p< 0.05
+p<0.05
+11
+10.0
+Encoder Errors
+7.5 
+5.0 
+2.5 
+0.0
+-2.5 
+-5.0 
+Control
+EL PD
+MD PD
+SV PD
+EL KOA
+MD KOA
+SV KOATable 6: Model performance for encoder, contextual and adversarial losses using standard
+metrics when the model trains with parkinson patients. Acc, Pre, Rec, Spe, Homo and Shape
+are for accuracy, precision, recall, specificity, homocedasticity and shapeness respectively.
+Loss
+Acc
+Pre
+Rec
+Spe
+Homo
+Shape
+ROC-AUC
+Encoder
+62.5%
+55.2%
+88.9%
+40.9%
+45%
+50%
+64.9%
+Contextual
+71.5%
+93.5%
+73.7%
+50%
+50%
+40%
+61.9%
+Adversarial
+68.8%
+64.1%
+69.4%
+68.2%
+45%
+40%
+68.8%
+ciation of expert diagnosis criteria. From an exhaustive experimental setup, the
+proposed approach was trained with videos recorded from a control population,
+while then parkinsonian patterns were associated with anomaly patterns from
+the design of a discrimination metric that operates from embedding represen-
+tations. From an owner dataset, the proposed approach achieves an ROC-AUC
+of 86.9%, while for an external dataset without unseen training videos, the
+proposed approach achieved an average ROC-AUC of 75%.
+One of the main issues addressed in this work was to make efforts to train
+generative architecture with a sufficient generalization capability to capture
+kinematic patterns without a bias associated to the capture setups. To carefully
+select such architectures, this study introduced homoscedasticity and shapeness
+as complementary statistical rules to validate the models. From these metrics
+was evidenced that encoder embeddings brings major capabilities to general-
+ize models, against the contextual and adversarial losses, achieving in average
+an 80% and 70% for homoscedasticity and shapeness, respectively. Once these
+metrics defined the best architecture and embedding representation, we confirm
+the selection by using the external dataset with different capture conditions and
+even with the study of a new disease class into the population i.e., the Knee-
+osteoarthritis. Remarkably, the proposed approach generates embeddings with
+sufficient capabilities to discriminate among different unseen populations.
+In the literature have been declared different efforts to develop computational
+strategies to discriminate parkinson from control patterns, following markerless
+and sensor-based observations [6–9, 22]. For instance, volumetric architectures
+have been adjusted from discriminatory rules taking minimization rules associ-
+ated with expert diagnosis annotations [6, 8]. These approaches have reported
+remarkable results (average an 95% ROC-AUC with 22 patients). Also, Sun
+et. al. proposed an architecture that takes frontal gait views and together with
+volumetric convolution layers, discriminates the level of freeze in the gait for
+parkinson patients with an accuracy of 79.3%. Likewise, Kour et. al. [22] de-
+velops a sensor-based approach to correlate postural relationships with several
+annotated disease groups (reports an accuracy = 92.4%, precision = 90.0% with
+14
+
+50 knee-ostheoarthritis, 16 parkinson and 30 control patients).
+Nonetheless,
+such schemes are restricted to a specific recording scenario and pose observa-
+tional configurations. Besides, the minimization of these representations may be
+biased by label annotations associated with expert diagnostics. Contrary, the
+proposed approach adjusts the representation using only control video sequences
+without any expert label intervention during the architecture tunning. In such
+case, the architecture has major flexibility to code potential hidden relation-
+ships associated with locomotor patterns. In fact, the proposed approach was
+validated with raw video sequences, reported in [22], surpassing precision scores
+without any additional training to observe such videos. Moreover, the proposed
+approach uses video sequences instead of representation from key points, that
+coarsely minimize dynamic complexity during locomotion.
+Recovered generalization metrics scores (homocedasticity = 80%, shapeness
+= 70% ) suggest that some patients have different statistical distributions, an
+expected result from variability in control population, as well as, the variability
+associated to disease parkinson phenotyping. In such sense, it is demanding
+a large set of training data to capture additional locomotion components, to-
+gether with a sufficient variability spectrum. Nonetheless, the re-training of the
+architecture should be supervised from output population distributions to avoid
+overfitting regarding specific training scenarios. The output reconstruction may
+also be extended as anomaly maps to evidence in the spatial domain the regions
+with anomalies, which further may represent some association with the disease
+to help experts in the correct identification of patient prediction.
+7. Conclusions
+This work presented a deep generative architecture with the capability of dis-
+covering anomaly locomotion patterns, convolving entire video sequences into a
+3D scheme. Interestingly, a parkinson disease population was projected to the
+architecture, returning not only outlier rejection but coding a new locomotion
+distribution with separable patterns with respect to the trained control popu-
+lation. These results evidenced a potential use of this learning and architecture
+scheme to recover potential digital biomarkers, coded into embedding represen-
+tations. The proposed approach was validated with standard classification rules
+but also with statistical measures to validate the capability of generalization.
+Future works include the validation of proposals among different stages and
+the use of federated scenarios with different experimental capture setups to test
+performance on real scenarios.
+8. Acknowledgements
+The authors thank Ministry of science, technology and innovation of Colom-
+bia (MINCIENCIAS) for supporting this research work by the project “Mecan-
+ismos computacionales de aprendizaje profundo para soportar tareas de local-
+izaci´on, segmentaci´on y pron´ostico de lesiones asociadas con accidentes cere-
+brovasculares isqu´emicos.”, with code 91934.
+15
+
+References
+[1] T. Vos, A. A. Abajobir, K. H. Abate, C. Abbafati, K. M. Abbas, F. Abd-
+Allah, R. S. Abdulkader, A. M. Abdulle, T. A. Abebo, S. F. Abera, et al.,
+Global, regional, and national incidence, prevalence, and years lived with
+disability for 328 diseases and injuries for 195 countries, 1990–2016: a sys-
+tematic analysis for the global burden of disease study 2016, The Lancet
+390 (10100) (2017) 1211–1259.
+[2] E. R. Dorsey, B. R. Bloem, The parkinson pandemic—a call to action,
+JAMA neurology 75 (1) (2018) 9–10.
+[3] W. H. Organization, Neurological disorders:
+public health challenges,
+World Health Organization, 2006.
+[4] R. Balestrino, A. Schapira, Parkinson disease, European journal of neurol-
+ogy 27 (1) (2020) 27–42.
+[5] N. Kour, S. Arora, et al., Computer-vision based diagnosis of parkinson’s
+disease via gait: a survey, IEEE Access 7 (2019) 156620–156645.
+[6] L. C. Guayac´an, E. Rangel, F. Mart´ınez, Towards understanding spatio-
+temporal parkinsonian patterns from salient regions of a 3d convolutional
+network, in: 2020 42nd Annual International Conference of the IEEE En-
+gineering in Medicine & Biology Society (EMBC), IEEE, 2020, pp. 3688–
+3691.
+[7] R. Sun, Z. Wang, K. E. Martens, S. Lewis, Convolutional 3d attention
+network for video based freezing of gait recognition, in: 2018 Digital Image
+Computing: Techniques and Applications (DICTA), IEEE, 2018, pp. 1–7.
+[8] L. C. Guayac´an, F. Mart´ınez, Visualising and quantifying relevant parkin-
+sonian gait patterns using 3d convolutional network, Journal of biomedical
+informatics 123 (2021) 103935.
+[9] M. H. Li, T. A. Mestre, S. H. Fox, B. Taati, Vision-based assessment of
+parkinsonism and levodopa-induced dyskinesia with pose estimation, Jour-
+nal of neuroengineering and rehabilitation 15 (1) (2018) 1–13.
+[10] G. Litjens, T. Kooi, B. E. Bejnordi, A. A. A. Setio, F. Ciompi, M. Ghafoo-
+rian, J. A. Van Der Laak, B. Van Ginneken, C. I. S´anchez, A survey on
+deep learning in medical image analysis, Medical image analysis 42 (2017)
+60–88.
+[11] K. Sugandhi, F. F. Wahid, G. Raju, Feature extraction methods for hu-
+man gait recognition–a survey, in: International Conference on Advances
+in Computing and Data Sciences, Springer, 2016, pp. 377–385.
+[12] R. Chalapathy, S. Chawla, Deep learning for anomaly detection: A survey,
+arXiv preprint arXiv:1901.03407 (2019).
+16
+
+[13] L. Schmarje, M. Santarossa, S.-M. Schr¨oder, R. Koch, A survey on semi-
+, self-and unsupervised learning for image classification, IEEE Access 9
+(2021) 82146–82168.
+[14] C.-W. Cho, W.-H. Chao, S.-H. Lin, Y.-Y. Chen, A vision-based analysis
+system for gait recognition in patients with parkinson’s disease, Expert
+Systems with applications 36 (3) (2009) 7033–7039.
+[15] S.-W. Chen, S.-H. Lin, L.-D. Liao, H.-Y. Lai, Y.-C. Pei, T.-S. Kuo, C.-T.
+Lin, J.-Y. Chang, Y.-Y. Chen, Y.-C. Lo, et al., Quantification and recogni-
+tion of parkinsonian gait from monocular video imaging using kernel-based
+principal component analysis, Biomedical engineering online 10 (1) (2011)
+1–21.
+[16] S. N˜omm, A. Toomela, M. Vaske, D. Uvarov, P. Taba, An alternative
+approach to distinguish movements of parkinson disease patients, IFAC-
+PapersOnLine 49 (19) (2016) 272–276.
+[17] S. Soltaninejad, A. Rosales-Castellanos, F. Ba, M. A. Ibarra-Manzano,
+I. Cheng, Body movement monitoring for parkinson’s disease patients us-
+ing a smart sensor based non-invasive technique, in: 2018 IEEE 20th In-
+ternational Conference on e-Health Networking, Applications and Services
+(Healthcom), IEEE, 2018, pp. 1–6.
+[18] B. R. Kiran, D. M. Thomas, R. Parakkal, An overview of deep learning
+based methods for unsupervised and semi-supervised anomaly detection in
+videos, Journal of Imaging 4 (2) (2018) 36.
+[19] J. Demˇsar, Statistical comparisons of classifiers over multiple data sets,
+The Journal of Machine Learning Research 7 (2006) 1–30.
+[20] J. Luengo, S. Garc´ıa, F. Herrera, A study on the use of statistical tests for
+experimentation with neural networks: Analysis of parametric test condi-
+tions and non-parametric tests, Expert Systems with Applications 36 (4)
+(2009) 7798–7808.
+[21] N. Kour, S. Arora, et al., A vision-based gait dataset for knee osteoarthritis
+and parkinson’s disease analysis with severity levels, in: International Con-
+ference on Innovative Computing and Communications, Springer, 2022, pp.
+303–317.
+[22] N. Kour, S. Gupta, S. Arora, A vision-based clinical analysis for classifica-
+tion of knee osteoarthritis, parkinson’s disease and normal gait with severity
+based on k-nearest neighbour, Expert Systems 39 (6) (2022) e12955.
+17
+

BNE3T4oBgHgl3EQfTwqq/vector_store/index.pkl

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ca0a33e4c68b080db9829e8e1c256e34898a4cd9904df9057f3a86cea39e86e9
+size 166251

BNE5T4oBgHgl3EQfTA98/content/2301.05533v1.pdf

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:1a17aa5c64af98e8d6f7e17c3b6b2da9364a35b25874e637cdcb131b1915c791
+size 941568

BNE5T4oBgHgl3EQfTA98/vector_store/index.faiss

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4cf5f4a17a6ca882e032c6fbab19853a8454e63850b5ce7a8a8a1c32eb38d5b5
+size 852013

BNE5T4oBgHgl3EQfTA98/vector_store/index.pkl

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:cd199afda7527e34448dce5487ac0c80ee7a5dea51a3f903e2f54e7970c06a23
+size 41563

C9E1T4oBgHgl3EQfWATV/content/2301.03110v1.pdf

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:7d17a499530c6190a1871f9eb504a8911739a804d0385a2aac125f0441f83ed0
+size 1377155

C9E1T4oBgHgl3EQfWATV/vector_store/index.pkl

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:8a5c488c72bab830d93fac033e963e507323f4155df21120e66027bc39069986
+size 255239

CdFQT4oBgHgl3EQfOTbk/content/2301.13275v1.pdf

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:4dde949a07417e038ce8268ecbe26a4319ce68064cddfc82d06003fc715f0d81
+size 404268

CdFQT4oBgHgl3EQfOTbk/vector_store/index.faiss

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:dfc4c560f82c3e7003ddecbef0bd8547d4585683f467db931523639dca8da8ab
+size 1966125

CdFQT4oBgHgl3EQfOTbk/vector_store/index.pkl

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:1db0d1197b51ac44f4a67dbc256be6b08bf86296f2313d2cfe9eaea3d19ecd6d
+size 72957

DNAzT4oBgHgl3EQfTvz-/content/2301.01257v1.pdf

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:fa35c8c396859145d37cd74882f13c06a429e5b69e218ed4b5ee23bc2d22b891
+size 901869

DNAzT4oBgHgl3EQfTvz-/vector_store/index.faiss

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:5fd5d64b5b788e7ab22a5b088be78d2fa3d3156c97fd230c07b63236f2651668
+size 4587565

DNAzT4oBgHgl3EQfTvz-/vector_store/index.pkl

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:16b5eceed0ddaf7fe53c4417076c602d56d406945d337dc6553dde809bfe881e
+size 162300

ENFRT4oBgHgl3EQfAze2/content/2301.13463v1.pdf

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:76147a92c2990565e70fdeb70a7abcca19991846f18910a252683b4b18b41c44
+size 226732

ENFRT4oBgHgl3EQfAze2/vector_store/index.pkl

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ca58edb41c3d7a419f2e1cbbcd7eb78b6838c5dd194825f9ddf77a189c542de2
+size 77172

EdE4T4oBgHgl3EQffQ16/vector_store/index.faiss

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:fa2bbdff342c0acfc83a62b878f786638eb75536ae7154a2aede5dcf2e55ff10
+size 1114157

EdE4T4oBgHgl3EQffQ16/vector_store/index.pkl

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:6424a1c4fc6684c50517b5ec1be24dd18b0bba04fa5586e191cd60a8ab6d5519
+size 47813

FdE3T4oBgHgl3EQfVwo4/content/2301.04462v1.pdf

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:abbd093abf47a6a39578390cbef636fbb441d86048ce0caf1265b7650ca5113a
+size 1613748