BP神经网络在python下的自主搭建梳理

本实验使用mnist数据集完成手写数字识别的测试。识别正确率认为是95%

完整代码如下：

#!/usr/bin/env python
# coding: utf-8

# In[1]:


import numpy
import scipy.special
import matplotlib.pyplot


# In[2]:


class neuralNetwork:
    def __init__(self, inputNodes, hiddenNodes, outputNodes,learningRate):
        self.iNodes = inputNodes
        self.oNodes = outputNodes
        self.hNodes = hiddenNodes
        self.lr = learningRate
        self.wih = numpy.random.normal (0.0, pow(self.hNodes,-0.5), (self.hNodes, self.iNodes))
        self.who = numpy.random.normal (0.0, pow(self.oNodes,-0.5), (self.oNodes, self.hNodes))
        
        self.activation_function = lambda x: scipy.special.expit(x)
        #print(self.wih)
        pass
    
    def train(self,inputs_list, target_list):
        inputs = numpy.array(inputs_list, ndmin=2).T
        targets = numpy.array(target_list, ndmin=2).T
        #print(inputs)
        #print(targets)
        hidden_inputs = numpy.dot(self.wih,inputs)
        #print(self.wih.shape)
        #print(inputs.shape)
        hidden_outputs = self.activation_function(hidden_inputs)
        #print(hidden_inputs)
        final_inputs = numpy.dot(self.who,hidden_outputs)
        #print(hidden_outputs)
        final_outputs = self.activation_function(final_inputs)
        
        output_errors = targets - final_outputs
        hidden_errors = numpy.dot(self.who.T,output_errors)
        self.who += self.lr * numpy.dot((output_errors * final_outputs * (1.0 - final_outputs)),numpy.transpose(hidden_outputs))
        self.wih += self.lr * numpy.dot((hidden_errors * hidden_outputs * (1.0 - hidden_outputs)),numpy.transpose(inputs))
        pass
    
    def query(self, inputs_list):
        inputs = numpy.array(inputs_list, ndmin=2).T
        hidden_inputs = numpy.dot(self.wih,inputs)
        hidden_outputs = self.activation_function(hidden_inputs)
        final_inputs = numpy.dot(self.who,hidden_outputs)
        final_outpus = self.activation_function(final_inputs)
        return final_outpus
        pass
    


# In[3]:


inputNodes = 784
outputNodes = 10
hiddenNodes = 100
learningRate = 0.1
nN = neuralNetwork(inputNodes, hiddenNodes, outputNodes, learningRate)


# In[4]:


data_file = open("mnist_train.csv",'r')
data_list = data_file.readlines()
data_file.close()


# In[5]:


epochs = 1
for e in range(epochs) :
    for record in data_list:
        all_values = record.split(',')
        inputs = numpy.asfarray( all_values [1:])/255.0*0.99+0.01
        targets = numpy.zeros(outputNodes) + 0.01
        targets[int (all_values[0])] = 0.99
        nN.train(inputs,targets)
        pass
    pass


# In[6]:


test_data_file = open("mnist_test.csv",'r')
test_data_list = test_data_file.readlines()
test_data_file.close()


# In[7]:


scorecard = []
for record in test_data_list:
    all_values = record.split(',')
    correct_label = int(all_values[0])
    inputs = numpy.asfarray( all_values [1:])/255.0*0.99+0.01
    outputs = nN.query(inputs)
    label = numpy.argmax(outputs)
    if(label == correct_label):
        scorecard.append(1)
    else:
        scorecard.append(0)
        pass
    pass


# In[8]:


scorecard_array = numpy.asarray(scorecard)
print ("performance = " ,scorecard_array.sum()/scorecard_array.size)


# In[9]:


import scipy.misc
img_array = scipy.misc.imread('test.png',flatten="True")
img_data = 255.0 - img_array . reshape(784)
img_data = (img_data /255.0 * 0.99 ) + 0.01
op=nN.query(img_data)
print(op)
print(numpy.argmax(op))


# In[10]:


all_values = data_list[1].split(',')
image_array = numpy.asfarray( all_values [1:]).reshape((28,28))
matplotlib.pyplot.imshow(image_array, cmap = 'Greys',interpolation='None')

IN[9]到IN[10]的代码分别用于测试自己制作的数字识别效果和显示图像。可去掉。

代码运行过程需要mnist数据集，链接：https://pan.baidu.com/s/120GTdZ8Tivkp1KD9VQ_XeQ

 BP神经网络的结构：https://www.cnblogs.com/bai2018/p/10353768.html

在输入层的神经元数据选取上，和像素数量一致。MNIST采用28X28的像素点，则输入层的神经元数量为28*28=784个

输入层和隐层，输出层和隐层之间的权值选取为随机数。使用正态分布的随机数较好。

隐层的神经元数量合适即可，取值为经验法，假设为100个

输出层神经元表示数据0-9，则使用10个神经元，分别表示数字0-9的可能性概率。

训练过程中使用的学习效率，取0.2吧。。。

将权重，各层神经元值，误差等，表示为矩阵数据进行处理。

正向传递数据查询结果，误差的反向传递改变权重等过程，涉及到的数学推导：https://www.cnblogs.com/bai2018/p/10353814.html