3层神经网络，自定义输入节点、隐藏层、输出节点的个数，使用sigmoid函数作为激活函数，梯度下降法进行权重的优化。

使用MNIST数据集，进行手写数字识别

1 #!/usr/bin/env python  2 # -*- coding:utf-8 -*-  3   4 #!/usr/bin/env python  5 # -*- coding:utf-8 -*-  6   7 import numpy  8 import scipy.special  9  10  11 #手写数字识别神经网络 12 class NeuralNetwork(): 13     def __init__(self,inputnodes,hiddennodes,outputnodes,learningrate): 14         ''' 15         神经网络初始化 16         :param inputnodes: 输入节点的数量 17         :param hiddennodes: 隐藏层节点的数量 18         :param outputnodes: 输出节点的数量 19         :param learningrate: 学习率 20         :return: 21         ''' 22         self.inodes = inputnodes 23         self.hnodes = hiddennodes 24         self.onodes = outputnodes 25         self.learn = learningrate 26         self.wih = numpy.random.rand(self.hnodes,self.inodes) - 0.5 27         self.who = numpy.random.rand(self.onodes,self.hnodes) - 0.5 28         # self.wih = numpy.random.normal(0.0,pow(self.hnodes,-0.5),(self.inodes,self.inodes)) 29         # self.who = numpy.random.normal(0.0,pow(self.onodes,-0.5),(self.hnodes,self.hnodes)) 30         self.activate_function = lambda x : scipy.special.expit(x) 31         # print(self.who) 32         # print(self.wih) 33     def train(self,input_list,target_list): 34         ''' 35         训练神经网络首先计算样本输出，然后在与目标值进行对比，更新权重 36         :param input_list: 输入值 37         :param target_list: 目标值 38         :return: 39         ''' 40         #针对样本计算输出，与query函数一样 41         inputs = numpy.array(input_list).T 42         targets = numpy.array(target_list).T 43         hidden_inputs = numpy.dot(self.wih,inputs) 44         hidden_outputs = self.activate_function(hidden_inputs) 45         final_inputs = numpy.dot(self.who,hidden_outputs) 46         final_outpust = self.activate_function(final_inputs) 47  48         #将计算得到的输出与目标值对比，更新权重 49         output_error = targets - final_outpust 50         hidden_error = numpy.dot(self.who.T,output_error) 51  52         # print(output_error.shape) 53         # print(final_outpust.shape) 54         # print(hidden_outputs.T.shape) 55         # self.who += self.learn*numpy.dot((output_error*final_outpust*(1.0-final_outpust)),numpy.transpose(hidden_outputs)) 56         # self.wih += self.learn*numpy.dot((hidden_error*hidden_outputs*(1.0-hidden_outputs)),numpy.transpose(inputs)) 57  58         self.who += self.learn*numpy.dot((output_error*final_outpust*(1.0-final_outpust)).reshape((self.onodes,1)),hidden_outputs.reshape((1,self.hnodes))) 59         self.wih += self.learn*numpy.dot((hidden_error*hidden_outputs*(1.0-hidden_outputs)).reshape((self.hnodes,1)),inputs.reshape((1,self.inodes))) 60  61  62  63     def query(self,input_list): 64         ''' 65         计算输出 66         :param input_list: 67         :return: 68         ''' 69         inputs = numpy.array(input_list).T 70         hidden_inputs = numpy.dot(self.wih,inputs) 71         hidden_outputs = self.activate_function(hidden_inputs) 72         final_inputs = numpy.dot(self.who,hidden_outputs) 73         final_outpust = self.activate_function(final_inputs) 74  75         return final_outpust 76  77 #初始化一个神经网络对象 78 n = NeuralNetwork(784,100,10,0.5) 79  80 #训练数据 81 with open('dataset/mnist_train.csv','r') as f: 82     train_data = f.readlines() 83  84 #训练神经网络 85 for line in train_data: 86     data = line.split(',') 87     inputs = (numpy.asfarray(data[1:]) / 255 * 0.99) + 0.01 88     targets = numpy.zeros(n.onodes)+0.01 89     targets[int(data[0])] = 0.99 90  91     n.train(inputs,targets) 92  93  94 #测试神经网络 95 with open('dataset/mnist_test_10.csv','r') as f: 96     test_data = f.readlines() 97  98 for line in test_data: 99     label = int(line[0])100     data = line.split(',')101     input_list = numpy.asfarray(data[1:])102     output = n.query(input_list)103 104     print(label)105     print(output)

代码实现了手写数字的识别，可以在此基础上，进行改进研究，比如调节学习率、初始化权重的方式，激活函数等变化时对结果的影响。