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--- |
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license: mit |
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language: |
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- zh |
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pipeline_tag: image-classification |
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--- |
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```python |
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import numpy as np |
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import scipy.special as ssp |
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import matplotlib.pyplot as plt |
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``` |
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```python |
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input_nodes=784 # 输入层节点数 |
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hide_nodes=200 # 隐藏层节点数,理论上越高越好，但是高到一定程度就到顶了（默认：200） |
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out_nodes=10 # 输出层节点数 |
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learningrate = 0.1 #学习率 |
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``` |
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```python |
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wih = np.random.normal(0.0, pow(hide_nodes, -0.5), (hide_nodes, input_nodes)) #矩阵大小为隐藏层节点数×输入层节点数 |
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#np.random.normal()的意思是一个正态分布，normal这里是正态的意思 |
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plt.hist(wih) |
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``` |
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(array([[ 1., 2., 3., ..., 8., 0., 0.], |
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[ 0., 0., 2., ..., 4., 0., 0.], |
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[ 0., 1., 5., ..., 9., 0., 0.], |
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..., |
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[ 0., 1., 2., ..., 10., 0., 0.], |
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[ 0., 1., 13., ..., 7., 0., 0.], |
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[ 0., 2., 8., ..., 3., 1., 0.]]), |
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array([-0.32167192, -0.25702275, -0.19237358, -0.12772441, -0.06307524, |
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0.00157393, 0.0662231 , 0.13087226, 0.19552143, 0.2601706 , |
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0.32481977]), |
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<a list of 784 BarContainer objects>) |
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```python |
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# Visualize weight matrix wih |
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plt.imshow(wih, cmap='coolwarm', aspect='auto') |
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#plt.imshow(wih, cmap='hot', aspect='auto') |
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plt.xlabel('Output Node') |
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plt.ylabel('Hidden Node') |
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plt.title('Weight Matrix (Hidden to input)') |
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plt.colorbar() |
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plt.show() |
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``` |
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```python |
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who = np.random.normal(0.0, pow(hide_nodes, -0.5), (out_nodes, hide_nodes)) #矩阵大小为输出层节点数×隐藏层节点数 |
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plt.hist(who) |
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#同上 |
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``` |
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(array([[0., 0., 1., ..., 0., 0., 0.], |
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[0., 0., 0., ..., 0., 0., 0.], |
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[0., 0., 0., ..., 1., 1., 0.], |
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..., |
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[0., 0., 0., ..., 1., 1., 0.], |
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[0., 0., 0., ..., 1., 0., 0.], |
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[0., 1., 2., ..., 0., 0., 0.]]), |
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array([-0.26261651, -0.21194208, -0.16126765, -0.11059322, -0.05991879, |
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-0.00924436, 0.04143007, 0.0921045 , 0.14277893, 0.19345336, |
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0.24412779]), |
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<a list of 200 BarContainer objects>) |
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```python |
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# Visualize weight matrix who |
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plt.imshow(who, cmap='coolwarm', aspect='auto') |
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plt.xlabel('Output Node') |
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plt.ylabel('Hidden Node') |
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plt.title('Weight Matrix (Hidden to Output)') |
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plt.colorbar() |
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plt.show() |
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``` |
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```python |
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#linspace 参考:https://blog.csdn.net/neweastsun/article/details/99676029 |
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x = np.linspace(start=-6, stop=6, num=121) #从-6到6范围内创建121个距离相近的数字，从而生成x数组用于代入后面的y |
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''' |
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e.g. |
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x = np.linspace(start = 0, stop = 100, num = 5) ##从0到100范围内创建5个距离相近的数字 |
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print(x) |
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OUT：[ 0. 25. 50. 75. 100.] |
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#lambda示例 |
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#lambda arg1,arg2,arg3… :<表达式> |
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func=lambda x : x+1 #func=x+1 |
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print(func(2)) #func=2+1=3 |
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func=lambda x,y : x+y #func=x+y |
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print(func(1,2)) #func=1+2=3 |
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''' |
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activation_function = lambda x: ssp.expit(x) #logistic sigmoid函数，定义为expit（x）= 1 /（1 + exp（-x）） |
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y = activation_function(x) |
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plt.plot(x, y) |
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plt.xlabel('x') |
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plt.title('logistic sigmoid(x)') |
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plt.show() |
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``` |
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```python |
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#数据集分为训练集和测试集，训练集有60000条数据，测试集有10000条数据， |
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#每一条数据都是由785个数字组成，数值大小在0~255之间，第一个数字代表该条数据所表示的数字， |
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#后面的784个数字可以形成28×28的矩阵(28x28=784)，每一个数值都对应该位置的像素点的像素值灰度大小，由此形成了一幅像素为28×28的图片。 |
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#这里是训练集 |
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test_data_file = open("mnist_train.csv", 'r') |
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test_data_list = test_data_file.readlines() |
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test_data_file.close() |
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print("总数据量:",len(test_data_list)) |
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print("第1条数据：",test_data_list[0]) |
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print("第1条数据表示的数字：",test_data_list[0][0]) |
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print("第1条数据的28x28矩阵数据:",test_data_list[0][1:]) |
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``` |
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总数据量: 60000 |
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第1条数据： 5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,18,18,18,126,136,175,26,166,255,247,127,0,0,0,0,0,0,0,0,0,0,0,0,30,36,94,154,170,253,253,253,253,253,225,172,253,242,195,64,0,0,0,0,0,0,0,0,0,0,0,49,238,253,253,253,253,253,253,253,253,251,93,82,82,56,39,0,0,0,0,0,0,0,0,0,0,0,0,18,219,253,253,253,253,253,198,182,247,241,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,80,156,107,253,253,205,11,0,43,154,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,14,1,154,253,90,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,139,253,190,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,11,190,253,70,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,35,241,225,160,108,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,81,240,253,253,119,25,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,45,186,253,253,150,27,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,16,93,252,253,187,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,249,253,249,64,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,46,130,183,253,253,207,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,39,148,229,253,253,253,250,182,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,24,114,221,253,253,253,253,201,78,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,23,66,213,253,253,253,253,198,81,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,18,171,219,253,253,253,253,195,80,9,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,55,172,226,253,253,253,253,244,133,11,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,136,253,253,253,212,135,132,16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 |
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第1条数据表示的数字： 5 |
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第1条数据的28x28矩阵数据: ,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,3,18,18,18,126,136,175,26,166,255,247,127,0,0,0,0,0,0,0,0,0,0,0,0,30,36,94,154,170,253,253,253,253,253,225,172,253,242,195,64,0,0,0,0,0,0,0,0,0,0,0,49,238,253,253,253,253,253,253,253,253,251,93,82,82,56,39,0,0,0,0,0,0,0,0,0,0,0,0,18,219,253,253,253,253,253,198,182,247,241,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,80,156,107,253,253,205,11,0,43,154,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,14,1,154,253,90,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,139,253,190,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,11,190,253,70,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,35,241,225,160,108,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,81,240,253,253,119,25,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,45,186,253,253,150,27,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,16,93,252,253,187,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,249,253,249,64,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,46,130,183,253,253,207,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,39,148,229,253,253,253,250,182,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,24,114,221,253,253,253,253,201,78,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,23,66,213,253,253,253,253,198,81,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,18,171,219,253,253,253,253,195,80,9,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,55,172,226,253,253,253,253,244,133,11,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,136,253,253,253,212,135,132,16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 |
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```python |
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all_values = test_data_list[0].split(',') # split()函数将第1条数据进行拆分，以‘，’为分界点进行拆分 |
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image_array = np.asfarray(all_values[1:]).reshape((28,28)) # asfarray()函数将all_values中的后784个数字进行重新排列 |
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# reshape()函数可以对数组进行整型，使其成为28×28的二维数组，asfarry()函数可以使其成为矩阵。 |
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plt.imshow(image_array, interpolation = 'nearest') # imshow()函数可以将28×28的矩阵中的数值当做像素值，使其形成图片 |
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``` |
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<matplotlib.image.AxesImage at 0x7fa3da4adfd0> |
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```python |
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#接下去是第1层和最后1层的逻辑 |
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``` |
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```python |
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# 对输入的数据进行处理，取后784个数据除以255，再乘以0.99，最后加上0。01，是所有的数据都在0.01到1.00之间 |
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inputs = (np.asfarray(all_values[1:]) / 255.0 * 0.99) + 0.01 #输入层，784个输入 |
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# 建立准确输出结果矩阵，对应的位置标签数值为0.99，其他位置为0.01 |
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#最终实现将0～255转换为0～1的浮点数 |
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#可视化中间输出 |
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print(inputs) |
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middle_layer_fig = np.asfarray((inputs-0.01)/0.99*255.0 ) |
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middle_layer_fig = np.asfarray(middle_layer_fig).reshape((28,28)) |
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plt.imshow(middle_layer_fig, interpolation = 'nearest') |
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``` |
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[0.01 0.01 0.01 0.01 0.01 0.01 |
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0.01 0.01 0.01 0.01 0.01 0.01 |
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0.01 0.01 0.01 0.01 0.01 0.01 |
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0.01 0.01 0.01 0.01 0.01 0.01 |
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0.01 0.01 0.01 0.01 0.01 0.01 |
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0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
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0.01 0.01 0.01 0.01 0.01 0.01 |
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0.01 0.01 0.01 0.01 0.01 0.01 |
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0.01 0.01 0.01 0.01 0.01 0.01 |
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0.01 0.01 0.02164706 0.07988235 0.07988235 0.07988235 |
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0.49917647 0.538 0.68941176 0.11094118 0.65447059 1. |
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0.96894118 0.50305882 0.01 0.01 0.01 0.01 |
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0.01 0.01 0.01 0.01 0.01 0.01 |
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0.01 0.01 0.12647059 0.14976471 0.37494118 0.60788235 |
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0.67 0.99223529 0.99223529 0.99223529 0.99223529 0.99223529 |
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0.88352941 0.67776471 0.99223529 0.94952941 0.76705882 0.25847059 |
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0.01 0.01 0.01 0.01 0.01 0.01 |
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0.01 0.01 0.01 0.01 0.01 0.20023529 |
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0.934 0.99223529 0.99223529 0.99223529 0.99223529 0.99223529 |
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0.99223529 0.99223529 0.99223529 0.98447059 0.37105882 0.32835294 |
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0.32835294 0.22741176 0.16141176 0.01 0.01 0.01 |
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0.01 0.01 0.01 0.01 0.01 0.01 |
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0.01 0.01 0.01 0.07988235 0.86023529 0.99223529 |
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0.99223529 0.99223529 0.99223529 0.99223529 0.77870588 0.71658824 |
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0.96894118 0.94564706 0.01 0.01 0.01 0.01 |
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0.01 0.01 0.01 0.01 0.01 0.01 |
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0.01 0.01 0.01 0.01 0.01 0.01 |
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0.01 0.01 0.32058824 0.61564706 0.42541176 0.99223529 |
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0.99223529 0.80588235 0.05270588 0.01 0.17694118 0.60788235 |
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0.01 0.01 0.01 0.01 0.01 0.01 |
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0.01 0.01 0.01 0.01 0.01 0.01 |
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0.01 0.01 0.01 0.01 0.01 0.01 |
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0.01 0.06435294 0.01388235 0.60788235 0.99223529 0.35941176 |
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0.01 0.01 0.01 0.01 0.01 0.01 |
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0.01 0.01 0.01 0.01 0.01 0.01 |
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0.01 0.01 0.01 0.01 0.01 0.01 |
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0.01 0.01 0.01 0.01 0.01 0.01 |
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0.01 0.54964706 0.99223529 0.74764706 0.01776471 0.01 |
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0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.05270588 |
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0.74764706 0.99223529 0.28176471 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.14588235 0.94564706 |
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0.88352941 0.63117647 0.42929412 0.01388235 0.01 0.01 |
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0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.32447059 0.94176471 0.99223529 |
|
0.99223529 0.472 0.10705882 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.18470588 0.73211765 0.99223529 0.99223529 |
|
0.59235294 0.11482353 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.07211765 0.37105882 0.98835294 0.99223529 0.736 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.97670588 0.99223529 0.97670588 0.25847059 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.18858824 0.51470588 0.72047059 0.99223529 |
|
0.99223529 0.81364706 0.01776471 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.16141176 0.58458824 |
|
0.89905882 0.99223529 0.99223529 0.99223529 0.98058824 0.71658824 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.10317647 0.45258824 0.868 0.99223529 0.99223529 0.99223529 |
|
0.99223529 0.79035294 0.31282353 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.09929412 0.26623529 0.83694118 0.99223529 |
|
0.99223529 0.99223529 0.99223529 0.77870588 0.32447059 0.01776471 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.07988235 0.67388235 |
|
0.86023529 0.99223529 0.99223529 0.99223529 0.99223529 0.76705882 |
|
0.32058824 0.04494118 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.22352941 0.67776471 0.88741176 0.99223529 0.99223529 0.99223529 |
|
0.99223529 0.95729412 0.52635294 0.05270588 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.538 0.99223529 |
|
0.99223529 0.99223529 0.83305882 0.53411765 0.52247059 0.07211765 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 0.01 0.01 |
|
0.01 0.01 0.01 0.01 ] |
|
|
|
|
|
|
|
|
|
|
|
<matplotlib.image.AxesImage at 0x7fa3da408d00> |
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|
 |
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|
|
```python |
|
targets = np.zeros(out_nodes) + 0.01 |
|
#输出层，10个数字，10个输出，0～1的概率范围 |
|
#输出层是1个list,由10个数字组成，第一个数字代表0的概率，依次类推，第10个数字代表9的概率 |
|
#这里是输出的[理想结果] |
|
# all_values[0] is the target label for this record |
|
#可视化中间输出 |
|
print(len(targets)) |
|
print(targets) |
|
middle_layer_fig = np.asfarray((targets-0.01)/0.99*255.0 ) |
|
middle_layer_fig = np.asfarray(middle_layer_fig).reshape((1,10)) |
|
plt.imshow(middle_layer_fig, interpolation = 'nearest') |
|
``` |
|
|
|
10 |
|
[0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01] |
|
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|
|
|
<matplotlib.image.AxesImage at 0x7fa3da3ad490> |
|
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|
 |
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|
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|
|
```python |
|
#print("第1行数据：",all_values) |
|
#print("第1行数据所表示的数字：",all_values[0]) |
|
targets[int(all_values[0])] = 0.99 |
|
#将数据集的数据表示的数字在其指定的输出层的概率位置上的概率置0.99 |
|
#这里是第1行数据，对应的是数组5，因此按照其在输出层的表示的概率位置，应当将第6个数字改为0.99 |
|
#可视化中间输出 |
|
print(targets) |
|
middle_layer_fig = np.asfarray((targets-0.01)/0.99*255.0 ) |
|
middle_layer_fig = np.asfarray(middle_layer_fig).reshape((1,10)) |
|
plt.imshow(middle_layer_fig, interpolation = 'nearest') |
|
``` |
|
|
|
[0.01 0.01 0.01 0.01 0.01 0.99 0.01 0.01 0.01 0.01] |
|
|
|
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|
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|
|
<matplotlib.image.AxesImage at 0x7fa3da30b4f0> |
|
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|
 |
|
|
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|
|
|
|
```python |
|
#对比 |
|
targets = np.zeros(out_nodes) + 0.01 |
|
print(targets) |
|
targets[int(all_values[0])] = 0.99 |
|
print(targets) |
|
``` |
|
|
|
[0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01] |
|
[0.01 0.01 0.01 0.01 0.01 0.99 0.01 0.01 0.01 0.01] |
|
|
|
|
|
|
|
```python |
|
#接下去是训练逻辑，训练的目标就是让输入的数据的概率尽可能接近理想结果 |
|
``` |
|
|
|
|
|
```python |
|
# 将导入的输入列表数据和正确的输出结果转换成二维矩阵 |
|
INPUT = np.array(inputs, ndmin = 2).T # array函数是矩阵生成函数，将输入的inputs转换成二维矩阵，ndmin=2表示二维矩阵 |
|
TARGETS = np.array(targets, ndmin = 2).T # .T表示矩阵的转置，生成后的矩阵的转置矩阵送入变量targets |
|
#print(INPUT) |
|
#print(TARGETS) |
|
``` |
|
|
|
|
|
```python |
|
# 进行前向传播 |
|
# 利用导入的数据计算进入隐藏层的数据 |
|
hidden_inputs = np.dot(wih, INPUT) # dot()函数是指两个矩阵做点乘 |
|
#可视化中间输出 |
|
print(hidden_inputs.T) |
|
# Visualize hidden layer activations |
|
#hidden_inputs = hidden_inputs.reshape((20, 10)) |
|
plt.imshow(hidden_inputs.T, cmap='hot', aspect='auto') |
|
plt.xlabel('Hidden Node') |
|
plt.ylabel('Sample') |
|
plt.title('Hidden Layer Activations') |
|
plt.colorbar() |
|
plt.show() |
|
``` |
|
|
|
[[-8.64964137e-01 -1.96617581e+00 7.43349647e-01 6.52699592e-01 |
|
3.90933284e-01 1.23038702e+00 -1.26960367e-01 -8.89064451e-01 |
|
1.25956352e-01 -2.66009122e-01 -3.87411628e-01 -8.55340714e-01 |
|
-3.73072385e-01 -4.88004264e-01 8.93519640e-01 -5.94015812e-01 |
|
-3.94940660e-01 -6.03127644e-01 -1.83468156e-01 1.21212338e+00 |
|
1.11156836e+00 -3.30592481e-03 -1.45441494e-01 -1.16176875e-01 |
|
-6.79873194e-01 1.35716864e-03 -9.88715475e-01 2.53326180e-01 |
|
7.95912751e-02 -8.71915904e-01 -4.99039240e-01 -9.32069427e-02 |
|
-1.29952079e+00 -1.18946859e-01 -2.22242548e-01 1.07578559e+00 |
|
1.69691315e-01 -4.42288856e-01 1.18089766e+00 3.81134469e-02 |
|
3.15796540e-01 1.07374634e+00 -7.71978830e-01 -1.77028239e-01 |
|
7.83445294e-01 1.16099348e+00 5.28529106e-01 -1.94025187e-02 |
|
2.00808369e-01 6.72844377e-01 1.21480995e+00 -2.05275063e-01 |
|
-1.02432531e+00 -1.40022847e+00 7.16467553e-01 -6.38000445e-01 |
|
-1.44617295e-01 4.72539610e-01 -6.51132050e-02 -1.02462391e+00 |
|
1.38454078e+00 7.12628876e-01 7.39171671e-02 -3.34221329e-01 |
|
5.03935486e-01 2.08522402e+00 2.29977865e-01 -8.58595299e-01 |
|
9.14983758e-01 5.27664003e-02 -3.49103724e-01 -1.29338789e+00 |
|
8.10453241e-01 2.08934398e+00 1.66835420e+00 -1.12660303e+00 |
|
-1.12181011e-01 1.70474734e-01 5.20577595e-01 6.00166910e-01 |
|
-3.81956593e-01 1.30122404e-01 -5.23356991e-01 -1.01661725e+00 |
|
-3.38834016e-01 6.30692963e-01 1.17169833e-01 9.13183907e-01 |
|
-1.10728477e+00 9.91458051e-01 -2.88315338e-01 7.70893096e-01 |
|
5.82703388e-01 -9.29590575e-02 -1.26294025e+00 1.94053320e-01 |
|
-5.96912464e-01 2.60424259e-01 4.29504575e-02 -7.60243022e-01 |
|
2.03240513e-02 7.27749904e-02 -7.19974851e-01 5.25634269e-01 |
|
-4.96678397e-01 -1.62713415e+00 2.89082887e-01 -5.26173924e-01 |
|
-3.82685176e-01 -1.76410064e+00 -1.33431697e+00 4.32481392e-01 |
|
2.33941967e+00 7.52802920e-01 2.17849572e-01 -8.38437665e-02 |
|
-5.51882457e-01 1.84692442e+00 -4.10696115e-01 3.97851800e-01 |
|
-1.49071923e-01 -2.81875633e-01 1.95378425e+00 -4.66989868e-01 |
|
-4.73375650e-01 1.66522535e-01 5.01408007e-01 -1.30089311e-01 |
|
1.44543864e+00 4.28063957e-01 3.86986466e-01 6.62182100e-01 |
|
-1.39480966e-01 -1.82625599e-01 -3.67218386e-01 -1.48826110e+00 |
|
-4.31214177e-01 -8.92040712e-01 -4.15032383e-01 -3.76042786e-01 |
|
-3.83971840e-01 7.49005651e-01 -3.16839497e-01 -7.70655367e-01 |
|
3.56918546e-01 -1.93469779e-01 -4.51644191e-01 -5.20009826e-01 |
|
7.61656212e-01 -5.39819400e-01 1.24457323e-01 4.02348827e-01 |
|
4.96390519e-02 -1.61507281e-01 -6.04062425e-01 4.77674466e-01 |
|
5.65500425e-01 -1.74931564e-02 1.82237163e-01 -2.52744493e-01 |
|
-9.74909666e-01 4.39247112e-01 2.50623145e-01 -5.47588554e-01 |
|
-1.10213410e+00 -7.96484480e-03 8.18154047e-01 -5.31161336e-01 |
|
9.45395512e-02 -4.80934079e-02 -4.15248499e-01 2.01334670e-02 |
|
-7.73149020e-01 5.16150140e-01 -1.11187297e+00 -3.84973353e-01 |
|
1.57056302e-01 9.52205562e-02 -4.17473666e-04 -2.64269971e-01 |
|
3.51661057e-02 -8.62097845e-01 -6.41290441e-01 -6.10216699e-01 |
|
1.48703377e+00 -9.36182669e-01 2.29758638e-01 2.69581850e-03 |
|
-9.90544195e-03 -1.16945542e-01 2.16055208e-01 -5.16034753e-01 |
|
-5.47460522e-01 1.21898405e+00 -1.40917054e-01 -1.10955125e+00 |
|
-1.06838867e+00 -8.16027514e-01 3.18583449e-01 7.11316110e-01]] |
|
|
|
|
|
|
|
|
|
 |
|
|
|
|
|
|
|
|
|
```python |
|
# 利用激活函数sigmoid计算隐藏层输出的数据 |
|
hidden_outputs = activation_function(hidden_inputs) |
|
#可视化中间输出 |
|
print(hidden_outputs.T) |
|
# Visualize hidden layer activations |
|
plt.imshow(hidden_outputs.T, cmap='hot', aspect='auto') |
|
plt.xlabel('Hidden Node') |
|
plt.ylabel('Sample') |
|
plt.title('Hidden Layer Activations') |
|
plt.colorbar() |
|
plt.show() |
|
``` |
|
|
|
[[0.29630324 0.12280024 0.6777279 0.65761855 0.59650735 0.7738863 |
|
0.46830247 0.29130293 0.53144752 0.43388711 0.40434055 0.29831372 |
|
0.40779883 0.38036382 0.70961597 0.35571397 0.40252851 0.35362846 |
|
0.45426119 0.77067444 0.75242139 0.49917352 0.46370359 0.4709884 |
|
0.33628961 0.50033929 0.27116587 0.56299502 0.51988732 0.2948558 |
|
0.37776648 0.47671512 0.21424568 0.4702983 0.44466693 0.74569562 |
|
0.54232132 0.39119572 0.76510917 0.50952721 0.5782995 0.74530871 |
|
0.3160512 0.45585816 0.68642218 0.76151319 0.62913998 0.49514952 |
|
0.55003407 0.66213977 0.77114891 0.44886068 0.26418574 0.19777986 |
|
0.67182867 0.34569868 0.46390856 0.61598467 0.48372745 0.2641277 |
|
0.79971928 0.67098178 0.51847088 0.41721386 0.62338374 0.88945871 |
|
0.55724239 0.29763291 0.71401891 0.51318854 0.41359978 0.21527993 |
|
0.69220608 0.88986315 0.84135627 0.24478854 0.47198412 0.54251577 |
|
0.62728282 0.64569449 0.40565508 0.53248478 0.37206759 0.26568684 |
|
0.41609274 0.65264657 0.52925899 0.71365125 0.24837744 0.72937582 |
|
0.42841635 0.68371406 0.64168922 0.47677696 0.22046816 0.54836166 |
|
0.35505039 0.56474058 0.51073596 0.31859351 0.50508084 0.51818572 |
|
0.32739852 0.6284643 0.37832157 0.16422333 0.57177159 0.3714097 |
|
0.40547943 0.14627751 0.20844618 0.60646605 0.91208956 0.67978913 |
|
0.55424802 0.47905133 0.36542777 0.86376559 0.39874522 0.59817142 |
|
0.46280088 0.429994 0.87585869 0.38532895 0.38381758 0.5415347 |
|
0.62279016 0.46752346 0.80929544 0.60541126 0.59555704 0.6597504 |
|
0.46518618 0.45447007 0.40921333 0.18418287 0.39383643 0.29068888 |
|
0.39770607 0.40708168 0.4051693 0.678962 0.42144618 0.31633735 |
|
0.5882943 0.45178286 0.38896992 0.37284994 0.68171321 0.3682296 |
|
0.53107423 0.59925186 0.51240722 0.45971072 0.35341483 0.61719858 |
|
0.63772427 0.49562682 0.54543362 0.4371481 0.27390298 0.60807962 |
|
0.56232987 0.36642406 0.24934024 0.4980088 0.69384436 0.37024607 |
|
0.5236173 0.48797896 0.3976543 0.5050332 0.3157983 0.6262471 |
|
0.24752187 0.40492795 0.53918356 0.52378717 0.49989563 0.43431435 |
|
0.50879062 0.29690123 0.34495489 0.35200977 0.81563264 0.28167207 |
|
0.5571883 0.50067395 0.49752366 0.47079689 0.55380467 0.37377991 |
|
0.36645379 0.77188471 0.46482892 0.24795456 0.25570964 0.30660756 |
|
0.57897899 0.67069191]] |
|
|
|
|
|
|
|
|
|
 |
|
|
|
|
|
|
|
|
|
```python |
|
# 利用隐藏层输出的数据计算导入输出层的数据 |
|
final_inputs = np.dot(who, hidden_outputs) # dot()函数是指两个矩阵做点乘 |
|
#可视化中间输出 |
|
print(final_inputs.T) |
|
middle_layer_fig = np.asfarray((final_inputs-0.01)/0.99*255.0 ) |
|
middle_layer_fig = np.asfarray(middle_layer_fig).reshape((1,10)) |
|
plt.imshow(middle_layer_fig, interpolation = 'nearest') |
|
``` |
|
|
|
[[ 0.56028136 0.82552015 0.34670209 0.17793798 -0.66372393 -0.37233255 |
|
-0.39555073 -0.76359914 -0.48399976 -0.23884983]] |
|
|
|
|
|
|
|
|
|
|
|
<matplotlib.image.AxesImage at 0x7fa3d89ffc10> |
|
|
|
|
|
|
|
|
|
|
|
 |
|
|
|
|
|
|
|
|
|
```python |
|
# Or visualize final outputs as a heatmap |
|
plt.imshow(final_inputs, cmap='hot', aspect='auto') |
|
plt.xlabel('Output Node') |
|
plt.ylabel('Sample') |
|
plt.title('Final Inputs') |
|
plt.colorbar() |
|
plt.show() |
|
``` |
|
|
|
|
|
|
|
 |
|
|
|
|
|
|
|
|
|
```python |
|
# Visualize final layer inputs |
|
plt.bar(range(out_nodes), final_inputs.flatten()) |
|
plt.xlabel('Output Node') |
|
plt.ylabel('Input Value') |
|
plt.title('Final Layer Inputs') |
|
plt.show() |
|
``` |
|
|
|
|
|
|
|
 |
|
|
|
|
|
|
|
|
|
```python |
|
# 利用激活函数sigmoid计算输出层的输出结果 |
|
final_outputs = activation_function(final_inputs) |
|
# 前向传播结束 |
|
|
|
#可视化中间输出 |
|
print(final_outputs.T) |
|
middle_layer_fig = np.asfarray((final_outputs-0.01)/0.99*255.0 ) |
|
middle_layer_fig = np.asfarray(middle_layer_fig).reshape((1,10)) |
|
plt.imshow(middle_layer_fig, interpolation = 'nearest') |
|
``` |
|
|
|
[[0.63651764 0.69540686 0.58581762 0.54436749 0.33990358 0.40797752 |
|
0.40238179 0.31786536 0.38130809 0.44056981]] |
|
|
|
|
|
|
|
|
|
|
|
<matplotlib.image.AxesImage at 0x7fa3da5f10a0> |
|
|
|
|
|
|
|
|
|
|
|
 |
|
|
|
|
|
|
|
|
|
```python |
|
# Or visualize final outputs as a heatmap |
|
plt.imshow(final_outputs, cmap='hot', aspect='auto') |
|
plt.xlabel('Output Node') |
|
plt.ylabel('Sample') |
|
plt.title('Final Outputs') |
|
plt.colorbar() |
|
plt.show() |
|
``` |
|
|
|
|
|
|
|
 |
|
|
|
|
|
|
|
|
|
```python |
|
# Visualize final layer outputs （sigmoid） |
|
plt.bar(range(out_nodes), final_outputs.flatten()) |
|
plt.xlabel('Output Node') |
|
plt.ylabel('Input Value') |
|
plt.title('Final Layer Inputs') |
|
plt.show() |
|
``` |
|
|
|
|
|
|
|
 |
|
|
|
|
|
|
|
|
|
```python |
|
# 进行反向传播 |
|
# 计算前向传播得到的输出结果与正确值之间的误差 |
|
output_errors = TARGETS - final_outputs |
|
|
|
#可视化中间输出 |
|
print(output_errors.T) |
|
middle_layer_fig = np.asfarray((output_errors-0.01)/0.99*255.0 ) |
|
middle_layer_fig = np.asfarray(middle_layer_fig).reshape((1,10)) |
|
plt.imshow(middle_layer_fig, interpolation = 'nearest') |
|
``` |
|
|
|
[[-0.62651764 -0.68540686 -0.57581762 -0.53436749 -0.32990358 0.58202248 |
|
-0.39238179 -0.30786536 -0.37130809 -0.43056981]] |
|
|
|
|
|
|
|
|
|
|
|
<matplotlib.image.AxesImage at 0x7fa3d87db8b0> |
|
|
|
|
|
|
|
|
|
|
|
 |
|
|
|
|
|
|
|
|
|
```python |
|
# Visualize output errors as a bar chart |
|
plt.bar(range(out_nodes), output_errors.flatten()) |
|
plt.xlabel('Output Node') |
|
plt.ylabel('Error Value') |
|
plt.title('Output Errors') |
|
plt.show() |
|
``` |
|
|
|
|
|
|
|
 |
|
|
|
|
|
|
|
|
|
```python |
|
# Or visualize output errors as a scatter plot |
|
plt.scatter(range(out_nodes), output_errors.flatten()) |
|
plt.xlabel('Output Node') |
|
plt.ylabel('Error Value') |
|
plt.title('Output Errors') |
|
plt.show() |
|
``` |
|
|
|
|
|
|
|
 |
|
|
|
|
|
|
|
|
|
```python |
|
# 隐藏层的误差是由输出层的误差通过两个层之间的权重矩阵进行分配的，在隐藏层重新结合 |
|
``` |
|
|
|
|
|
```python |
|
hidden_errors = np.dot(who.T, output_errors) # 隐藏层与输出层之间的权重矩阵的转置与前向传播的误差矩阵的点乘 |
|
#可视化中间输出 |
|
print(hidden_errors.T) |
|
#middle_layer_fig = np.asfarray((hidden_errors-0.01)/0.99*255.0 ) |
|
#middle_layer_fig = np.asfarray(middle_layer_fig).reshape((20,10)) |
|
#plt.imshow(middle_layer_fig, interpolation = 'nearest') |
|
``` |
|
|
|
[[ 0.23145703 -0.09199276 -0.12220719 -0.15896069 0.06424253 0.10197068 |
|
-0.23125848 -0.00782811 -0.08381227 -0.11514534 -0.09644854 -0.12429981 |
|
0.11276763 -0.26363747 -0.00989155 -0.14107911 0.27482566 0.10077863 |
|
0.08727872 -0.12703169 0.04482464 0.07979755 -0.08780178 -0.10513761 |
|
-0.00644824 -0.11657829 -0.04453468 0.05577635 0.01531368 0.13738715 |
|
0.03474212 0.22550981 -0.08763767 -0.06505764 -0.11262462 -0.04158586 |
|
-0.09128322 -0.01086248 0.05525096 -0.12434499 0.17656152 0.04339815 |
|
-0.03433653 -0.11152836 0.03669448 -0.01467246 0.01413861 0.17155288 |
|
-0.12223192 -0.10968683 0.10515451 0.14353315 0.08262463 0.16657906 |
|
-0.10807233 -0.10796653 -0.01689826 0.05175527 -0.02711501 -0.06925127 |
|
0.24918363 -0.0658346 -0.01650576 -0.14181141 -0.06328054 0.11752269 |
|
0.07361948 -0.25658514 -0.03837734 0.05291595 0.18022871 -0.02485894 |
|
-0.11155773 -0.17969543 0.05235072 -0.03868002 0.07991305 -0.00944794 |
|
0.01358124 -0.04854606 -0.11433062 -0.11457118 -0.10174756 0.08157923 |
|
-0.07922054 0.16252699 -0.0668835 0.02633577 -0.25292949 -0.00164063 |
|
0.17719827 -0.27838094 0.06372956 -0.08327759 -0.1045452 0.0994223 |
|
-0.18854096 0.01717639 -0.22337965 -0.05331426 -0.09068925 0.00909319 |
|
-0.11275048 0.02400681 0.15580461 0.04395622 0.05191163 0.07671998 |
|
-0.07357827 0.04857611 0.01200461 -0.01824155 0.20218933 -0.01648541 |
|
-0.08841815 -0.22972757 -0.06564815 0.25879827 0.03363929 -0.08144042 |
|
-0.00117747 0.04931258 -0.28733007 0.09207885 -0.11084745 0.03480787 |
|
-0.30290225 0.02605289 -0.03273764 0.13374028 0.06733113 -0.08264645 |
|
-0.10579 -0.16626817 -0.19349467 0.2339928 0.25338442 -0.04781617 |
|
0.01431193 -0.06614716 -0.03706169 -0.18027598 0.03546684 0.07375848 |
|
-0.13524866 -0.14490857 -0.21459248 0.1796899 0.02376605 -0.02517879 |
|
0.00632407 0.03003414 -0.11537092 0.03510202 0.07357026 0.0971219 |
|
-0.08266574 0.03720117 0.09910707 -0.04312925 -0.08307132 0.02983252 |
|
0.01496464 0.07249455 -0.1618727 0.11377448 -0.03207163 0.19216192 |
|
0.09118743 0.01690548 -0.06923089 0.02959015 0.20129512 -0.04899694 |
|
0.1233579 -0.20508642 0.01812198 -0.00063595 0.17360329 0.11723159 |
|
0.15777609 0.07835488 -0.05387801 -0.01755501 0.10815374 0.22098465 |
|
-0.12040005 0.025853 -0.08475004 0.24887947 0.07332807 0.0784619 |
|
0.01351764 -0.08704183 0.08712977 0.0756019 -0.04051772 -0.15931343 |
|
-0.04228901 0.13588616]] |
|
|
|
|
|
|
|
```python |
|
# Visualize hidden errors as a bar chart |
|
plt.bar(range(hide_nodes), hidden_errors.flatten()) |
|
plt.xlabel('Hidden Node') |
|
plt.ylabel('Error Value') |
|
plt.title('Hidden Errors') |
|
plt.show() |
|
``` |
|
|
|
|
|
|
|
 |
|
|
|
|
|
|
|
|
|
```python |
|
# Or visualize hidden errors as a scatter plot |
|
plt.scatter(range(hide_nodes), hidden_errors.flatten()) |
|
plt.xlabel('Hidden Node') |
|
plt.ylabel('Error Value') |
|
plt.title('Hidden Errors') |
|
plt.show() |
|
``` |
|
|
|
|
|
|
|
 |
|
|
|
|
|
|
|
|
|
```python |
|
# 对隐藏层与输出层之间的权重矩阵进行更新迭代 |
|
who += learningrate * np.dot((output_errors * final_outputs * (1.0 - final_outputs)),np.transpose(hidden_outputs)) |
|
# 对输入层与隐藏层之间的权重矩阵进行更新迭代 |
|
wih += learningrate * np.dot((hidden_errors * hidden_outputs * (1.0 - hidden_outputs)), np.transpose(INPUT)) |
|
``` |
|
|
|
|
|
```python |
|
#第一次迭代训练结束 |
|
print(wih) |
|
print(who) |
|
``` |
|
|
|
[[ 0.02067233 -0.07978803 0.03108053 ... -0.03073812 0.0557655 |
|
-0.05129495] |
|
[ 0.07106607 0.08339657 -0.09380426 ... 0.0441884 -0.03837313 |
|
-0.08557481] |
|
[ 0.05502248 -0.09130093 0.0384007 ... -0.00538593 0.06249898 |
|
0.08624116] |
|
... |
|
[-0.00994263 -0.07816935 -0.01082394 ... 0.00301429 -0.00230436 |
|
0.09999818] |
|
[ 0.03612263 -0.01946694 0.0954403 ... 0.01146139 -0.00025476 |
|
-0.12006706] |
|
[-0.05983042 -0.01998364 -0.06092712 ... -0.02392167 -0.06806361 |
|
0.01094472]] |
|
[[-0.0204511 -0.07749507 -0.00194097 ... 0.09540347 0.008829 |
|
-0.02140005] |
|
[-0.01264093 0.06889351 0.04956639 ... -0.0669025 -0.01843888 |
|
0.00722866] |
|
[-0.05481193 0.04000967 -0.09688887 ... 0.07287872 0.11162873 |
|
-0.12241058] |
|
... |
|
[-0.0972931 0.05829893 0.13900051 ... 0.04472318 0.0444388 |
|
-0.1383636 ] |
|
[ 0.0109094 0.01127165 0.00850074 ... 0.00947806 -0.08093348 |
|
-0.17257885] |
|
[-0.08861324 0.04998882 0.03560659 ... 0.05427103 -0.06461784 |
|
0.01395731]] |
|
|
|
|
|
|
|
```python |
|
print(wih) |
|
# Visualize weight matrix wih |
|
plt.imshow(wih, cmap='coolwarm', aspect='auto') |
|
plt.xlabel('Output Node') |
|
plt.ylabel('Hidden Node') |
|
plt.title('Weight Matrix (Hidden to input)') |
|
plt.colorbar() |
|
plt.show() |
|
``` |
|
|
|
[[ 0.02067233 -0.07978803 0.03108053 ... -0.03073812 0.0557655 |
|
-0.05129495] |
|
[ 0.07106607 0.08339657 -0.09380426 ... 0.0441884 -0.03837313 |
|
-0.08557481] |
|
[ 0.05502248 -0.09130093 0.0384007 ... -0.00538593 0.06249898 |
|
0.08624116] |
|
... |
|
[-0.00994263 -0.07816935 -0.01082394 ... 0.00301429 -0.00230436 |
|
0.09999818] |
|
[ 0.03612263 -0.01946694 0.0954403 ... 0.01146139 -0.00025476 |
|
-0.12006706] |
|
[-0.05983042 -0.01998364 -0.06092712 ... -0.02392167 -0.06806361 |
|
0.01094472]] |
|
|
|
|
|
|
|
|
|
 |
|
|
|
|
|
|
|
|
|
```python |
|
print(who) |
|
# Visualize weight matrix who |
|
plt.imshow(who, cmap='coolwarm', aspect='auto') |
|
plt.xlabel('Output Node') |
|
plt.ylabel('Hidden Node') |
|
plt.title('Weight Matrix (Hidden to Output)') |
|
plt.colorbar() |
|
plt.show() |
|
``` |
|
|
|
[[-0.0204511 -0.07749507 -0.00194097 ... 0.09540347 0.008829 |
|
-0.02140005] |
|
[-0.01264093 0.06889351 0.04956639 ... -0.0669025 -0.01843888 |
|
0.00722866] |
|
[-0.05481193 0.04000967 -0.09688887 ... 0.07287872 0.11162873 |
|
-0.12241058] |
|
... |
|
[-0.0972931 0.05829893 0.13900051 ... 0.04472318 0.0444388 |
|
-0.1383636 ] |
|
[ 0.0109094 0.01127165 0.00850074 ... 0.00947806 -0.08093348 |
|
-0.17257885] |
|
[-0.08861324 0.04998882 0.03560659 ... 0.05427103 -0.06461784 |
|
0.01395731]] |
|
|
|
|
|
|
|
|
|
 |
|
|
|
|
|
|
|
|
|
```python |
|
#完整训练流程 |
|
``` |
|
|
|
|
|
```python |
|
input_nodes=784 # 输入层节点数 |
|
hide_nodes=200 # 隐藏层节点数 |
|
out_nodes=10 # 输出层节点数 |
|
learningrate = 0.1 #学习率 |
|
train_errors = [] |
|
epochs=5 |
|
|
|
wih = np.random.normal(0.0, pow(hide_nodes, -0.5), (hide_nodes, input_nodes)) #矩阵大小为隐藏层节点数×输入层节点数 |
|
#np.random.normal()的意思是一个正态分布，normal这里是正态的意思 |
|
who = np.random.normal(0.0, pow(hide_nodes, -0.5), (out_nodes, hide_nodes)) #矩阵大小为输出层节点数×隐藏层节点数 |
|
activation_function = lambda x: ssp.expit(x) #结合上述所学，这里写一段原理是logistic sigmoid的激活函数 |
|
|
|
test_data_file = open("mnist_train.csv", 'r') |
|
test_data_list = test_data_file.readlines() |
|
test_data_file.close() |
|
|
|
for e in range(epochs): |
|
# go through all records in the training data set |
|
# 遍历所有输入的数据 |
|
print('epochs start:',e) |
|
# 计算训练集上的误差 |
|
train_error = 0.0 |
|
for record in test_data_list: |
|
all_values = record.split(',') # split()函数将第1条数据进行拆分，以‘，’为分界点进行拆分 |
|
inputs = (np.asfarray(all_values[1:]) / 255.0 * 0.99) + 0.01 #输入层，784个输入 |
|
targets = np.zeros(out_nodes) + 0.01 |
|
targets[int(all_values[0])] = 0.99 |
|
INPUT = np.array(inputs, ndmin = 2).T # array函数是矩阵生成函数，将输入的inputs转换成二维矩阵，ndmin=2表示二维矩阵 |
|
TARGETS = np.array(targets, ndmin = 2).T # .T表示矩阵的转置，生成后的矩阵的转置矩阵送入变量targets |
|
# 进行前向传播 |
|
# 利用导入的数据计算进入隐藏层的数据 |
|
hidden_inputs = np.dot(wih, INPUT) # dot()函数是指两个矩阵做点乘 |
|
# 利用激活函数sigmoid计算隐藏层输出的数据 |
|
hidden_outputs = activation_function(hidden_inputs) |
|
# 利用隐藏层输出的数据计算导入输出层的数据 |
|
final_inputs = np.dot(who, hidden_outputs) # dot()函数是指两个矩阵做点乘 |
|
# 利用激活函数sigmoid计算输出层的输出结果 |
|
final_outputs = activation_function(final_inputs) |
|
# 前向传播结束 |
|
# 进行反向传播 |
|
# 计算前向传播得到的输出结果与正确值之间的误差 |
|
output_errors = TARGETS - final_outputs |
|
# 隐藏层的误差是由输出层的误差通过两个层之间的权重矩阵进行分配的，在隐藏层重新结合 |
|
hidden_errors = np.dot(who.T, output_errors) # 隐藏层与输出层之间的权重矩阵的转置与前向传播的误差矩阵的点乘 |
|
# 对隐藏层与输出层之间的权重矩阵进行更新迭代 |
|
who += learningrate * np.dot((output_errors * final_outputs * (1.0 - final_outputs)),np.transpose(hidden_outputs)) |
|
# 对输入层与隐藏层之间的权重矩阵进行更新迭代 |
|
wih += learningrate * np.dot((hidden_errors * hidden_outputs * (1.0 - hidden_outputs)), np.transpose(INPUT)) |
|
train_error += np.sum((output_errors) ** 2) |
|
train_error /= len(test_data_list) |
|
train_errors.append(train_error) |
|
|
|
# 画出误差曲线 |
|
plt.plot(train_errors, label='training error') |
|
plt.legend() |
|
plt.show() |
|
``` |
|
|
|
epochs start: 0 |
|
epochs start: 1 |
|
epochs start: 2 |
|
epochs start: 3 |
|
epochs start: 4 |
|
|
|
|
|
|
|
|
|
 |
|
|
|
|
|
|
|
|
|
```python |
|
#最终结果,这两个变量就是最终的权重(weights) |
|
print(who) |
|
print(wih) |
|
final_who=who |
|
final_wih=wih |
|
``` |
|
|
|
[[-1.16611326 -0.4525141 -0.06610833 ... -0.45357449 -0.48939251 |
|
0.64537313] |
|
[-0.23350166 -0.07640343 -0.33892076 ... -0.42012762 -0.09425477 |
|
-0.35624211] |
|
[ 0.02538154 -0.36034837 -0.31796842 ... -0.03179198 0.24630403 |
|
0.53641215] |
|
... |
|
[-0.62273744 1.44743377 0.37902492 ... -1.22510993 0.85708252 |
|
-0.0379783 ] |
|
[-0.30649461 -0.45335212 -0.75158325 ... 0.27636151 -0.47017666 |
|
-0.43715161] |
|
[ 0.01993143 -1.11644346 1.10811109 ... 0.39435807 -0.77164373 |
|
-0.37836149]] |
|
[[ 0.01027389 -0.06948278 -0.13336783 ... 0.0431249 0.0116984 |
|
0.01118535] |
|
[ 0.04093141 0.13349408 0.0447183 ... -0.02876729 -0.08677845 |
|
-0.05826928] |
|
[-0.11370514 -0.04104104 0.05438874 ... -0.00457712 -0.01669163 |
|
-0.02552346] |
|
... |
|
[-0.00480138 0.04369124 -0.07553194 ... 0.09218518 0.02003152 |
|
0.0808828 ] |
|
[-0.00826098 0.07729079 -0.12576362 ... 0.03445958 0.02413203 |
|
-0.08935369] |
|
[-0.03758297 -0.06222281 0.02554687 ... 0.13169544 0.01547494 |
|
-0.07650541]] |
|
|
|
|
|
|
|
```python |
|
#保存权重 |
|
np.save("weights", final_who) |
|
np.save("weights02",final_wih) |
|
``` |
|
|
|
|
|
```python |
|
#测试 |
|
``` |
|
|
|
|
|
```python |
|
#加载权重文件(weights) |
|
final_who=np.load("weights.npy") |
|
final_wih=np.load("weights02.npy") |
|
``` |
|
|
|
|
|
```python |
|
# Visualize weight matrix wih |
|
plt.imshow(final_wih, cmap='coolwarm', aspect='auto') |
|
plt.xlabel('Output Node') |
|
plt.ylabel('Hidden Node') |
|
plt.title('Weight Matrix (Hidden to input)') |
|
plt.colorbar() |
|
plt.show() |
|
``` |
|
|
|
|
|
|
|
 |
|
|
|
|
|
|
|
|
|
```python |
|
# Visualize weight matrix who |
|
plt.imshow(final_who, cmap='coolwarm', aspect='auto') |
|
plt.xlabel('Output Node') |
|
plt.ylabel('Hidden Node') |
|
plt.title('Weight Matrix (Hidden to output)') |
|
plt.colorbar() |
|
plt.show() |
|
``` |
|
|
|
|
|
|
|
 |
|
|
|
|
|
|
|
|
|
```python |
|
test_data_file = open("mnist_test.csv", 'r') |
|
test_data_list = test_data_file.readlines() |
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test_data_file.close() |
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``` |
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```python |
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data_serial_num=455 |
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all_values = test_data_list[data_serial_num].split(',') # split()函数将第1条数据进行拆分，以‘，’为分界点进行拆分 |
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inputs = (np.asfarray(all_values[1:]) / 255.0 * 0.99) + 0.01 |
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#print(inputs) |
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image_array = np.asfarray(all_values[1:]).reshape((28,28)) # asfarray()函数将all_values中的后784个数字进行重新排列 |
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# reshape()函数可以对数组进行整型，使其成为28×28的二维数组，asfarry()函数可以使其成为矩阵。 |
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plt.imshow(image_array, interpolation = 'nearest') # imshow()函数可以将28×28的矩阵中的数值当做像素值，使其形成图片 |
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``` |
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<matplotlib.image.AxesImage at 0x7fa3d809b2e0> |
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```python |
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test_inputs = np.array(inputs, ndmin = 2).T |
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# 以下程序为计算输出结果的程序，与上面前向传播算法一致 |
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hidden_inputs = np.dot(final_wih, test_inputs) |
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hidden_outputs = activation_function(hidden_inputs) |
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final_inputs = np.dot(final_who, hidden_outputs) |
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final_outputs = activation_function(final_inputs) |
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print(final_outputs) |
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``` |
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[[0.01072488] |
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[0.99333831] |
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[0.00781424] |
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[0.00584866] |
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[0.02362064] |
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[0.01216366] |
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[0.00683059] |
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[0.00921785] |
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[0.00169813] |
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[0.00730339]] |
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```python |
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# Visualize hidden layer activations |
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#hidden_inputs = hidden_inputs.reshape((20, 10)) |
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plt.imshow(hidden_inputs.T, cmap='hot', aspect='auto') |
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plt.xlabel('Hidden Node') |
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plt.ylabel('Sample') |
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plt.title('Hidden Layer Activations') |
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plt.colorbar() |
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plt.show() |
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``` |
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 |
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```python |
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# Visualize hidden layer activations |
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plt.imshow(hidden_outputs.T, cmap='hot', aspect='auto') |
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plt.xlabel('Hidden Node') |
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plt.ylabel('Sample') |
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plt.title('Hidden Layer Activations') |
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plt.colorbar() |
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plt.show() |
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``` |
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```python |
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#可视化中间输出 |
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print(final_inputs.T) |
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middle_layer_fig = np.asfarray((final_inputs-0.01)/0.99*255.0 ) |
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middle_layer_fig = np.asfarray(middle_layer_fig).reshape((1,10)) |
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plt.imshow(middle_layer_fig, interpolation = 'nearest') |
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``` |
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|
[[-4.52440665 5.00469803 -4.84396237 -5.13567656 -3.72173031 -4.39706459 |
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-4.97949043 -4.67735268 -6.37652596 -4.91208681]] |
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<matplotlib.image.AxesImage at 0x7fa3cbe083a0> |
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```python |
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# Or visualize final outputs as a heatmap |
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plt.imshow(final_inputs, cmap='hot', aspect='auto') |
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plt.xlabel('Input Node') |
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plt.ylabel('Sample') |
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plt.title('Final Inputs') |
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plt.colorbar() |
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plt.show() |
|
``` |
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 |
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```python |
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# Visualize final layer inputs |
|
plt.bar(range(out_nodes), final_inputs.flatten()) |
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plt.xlabel('Output Node') |
|
plt.ylabel('Input Value') |
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plt.title('Final Layer Inputs') |
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plt.show() |
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``` |
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```python |
|
#可视化中间输出 |
|
print(final_outputs.T) |
|
middle_layer_fig = np.asfarray((final_outputs-0.01)/0.99*255.0 ) |
|
middle_layer_fig = np.asfarray(middle_layer_fig).reshape((1,10)) |
|
plt.imshow(middle_layer_fig, interpolation = 'nearest') |
|
``` |
|
|
|
[[0.01072488 0.99333831 0.00781424 0.00584866 0.02362064 0.01216366 |
|
0.00683059 0.00921785 0.00169813 0.00730339]] |
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|
<matplotlib.image.AxesImage at 0x7fa3cbcba550> |
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|
 |
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|
```python |
|
# Or visualize final outputs as a heatmap |
|
plt.imshow(final_outputs, cmap='hot', aspect='auto') |
|
plt.xlabel('Output Node') |
|
plt.ylabel('Sample') |
|
plt.title('Final Outputs') |
|
plt.colorbar() |
|
plt.show() |
|
``` |
|
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|
 |
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|
```python |
|
# Visualize final layer outputs （sigmoid） |
|
plt.bar(range(out_nodes), final_outputs.flatten()) |
|
plt.xlabel('Output Node') |
|
plt.ylabel('Input Value') |
|
plt.title('Final Layer Outputs') |
|
plt.show() |
|
``` |
|
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|
 |
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|
```python |
|
lebal = np.argmax(final_outputs) |
|
print(lebal) |
|
``` |
|
|
|
1 |
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|
|
```python |
|
#模型效果和性能测试 |
|
``` |
|
|
|
|
|
```python |
|
# load the mnist test data CSV file into a list |
|
# 导入测试集数据 |
|
test_data_file = open("mnist_test.csv", 'r') |
|
test_data_list = test_data_file.readlines() |
|
test_data_file.close() |
|
# test the neural network |
|
# 用query函数对测试集进行检测 |
|
# go through all the records in the test data set for record in the test_data_list: |
|
scorecard = 0 # 得分卡，检测对一个加一分 |
|
# 计算测试集上的误差 |
|
|
|
for record in test_data_list: |
|
# split the record by the ',' comas |
|
# 将所有测试数据通过逗号分隔开 |
|
all_values = record.split(',') |
|
# correct answer is first value |
|
# 正确值为每一条测试数据的第一个数值 |
|
correct_lebal = int(all_values[0]) |
|
#print("correct lebal", correct_lebal) # 将正确的数值在屏幕上打印出来 |
|
# scale and shift the inputs |
|
# 对输入数据进行处理，取后784个数据除以255，再乘以0.99，最后加上0。01，是所有的数据都在0.01到1.00之间 |
|
inputs = (np.asfarray(all_values[1:]) / 255.0 * 0.99) + 0.01 #输入层，784个输入 |
|
|
|
# query the network |
|
# 用query函数对测试集进行检测 |
|
|
|
test_inputs = np.array(inputs, ndmin = 2).T |
|
# 以下程序为计算输出结果的程序，与上面前向传播算法一致 |
|
hidden_inputs = np.dot(final_wih, test_inputs) |
|
hidden_outputs = activation_function(hidden_inputs) |
|
final_inputs = np.dot(final_who, hidden_outputs) |
|
final_outputs = activation_function(final_inputs) |
|
|
|
# the index of the highest value corresponds to out label |
|
# 得到的数字就是输出结果的最大的数值所对应的标签 |
|
lebal = np.argmax(final_outputs) # argmax()函数用于找出数值最大的值所对应的标签 |
|
#print("Output is ", lebal) # 在屏幕上打出最终输出的结果 |
|
# output image of every digit |
|
# 输出每一个数字的图片 |
|
#image_correct = np.asfarray(all_values[1:]).reshape((28, 28)) |
|
#plt.imshow(image_correct, cmap = 'Greys', interpolation = 'None') |
|
#plt.show() |
|
# append correct or incorrect to list |
|
if (lebal == correct_lebal): |
|
# network's answer matchs correct answer, add 1 to scorecard |
|
scorecard += 1 |
|
else: |
|
# network's answer doesn't match correct answer, add 0 to scorecard |
|
scorecard += 0 |
|
pass |
|
pass |
|
|
|
# calculate the performance score, the fraction |
|
# 计算准确率 得分卡最后的数值/10000（测试集总个数） |
|
print("performance = ", scorecard / 10000) |
|
|
|
``` |
|
|
|
performance = 0.9722 |
|
|
|
|
|
|
|
|
