代码来源：《Python神经网络编程》 手写数据集下载地址: 1.训练数据集 2.测试数据集

摘要

本文代码主要讲解基于Python的简单神经网络构建用于识别手写数据集，类模块具有通用性，在分析清楚问题后可以加以改动，运用于其他方面。

代码

import numpy # scipy.special for the sigmoid function expit() import scipy.special import matplotlib.pyplot as plt # neural network class definition class neuralNetwork: # initialise the neural network def __init__(self, inputnodes, hiddennodes, outputnodes, learningrate): # set number of nodes in each input, hidden, output layer self.inodes = inputnodes self.hnodes = hiddennodes self.onodes = outputnodes # link weight matrices, wih and who # weight inside the arrays are w_i_j, where link is from node i to node j in the next layer # w11 w21 # w12 w22 etc # 创建的两个链接权重矩阵 # self.wih = (numpy.random.rand(self.hnodes, self.inodes) - 0.5) # self.who = (numpy.random.rand(self.onodes, self.hnodes) - 0.5) # 正态分布初始化值，第一个参数表示正态分布中心，第二个参数表示标准方差，第三个参数表示形状 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)) # learning rate self.lr = learningrate # activation function is the sigmoid function # 相当于创建一个函数，函数接收x，返回scipy.special.expit(x)，调用时使用self.activation_function(...)即可 self.activation_function = lambda x: scipy.special.expit(x) pass # train the neural network def train(self, inputs_list, targets_list): # convert inputs list to 2d array inputs = numpy.array(inputs_list, ndmin=2).T targets = numpy.array(targets_list, ndmin=2).T # calculate signals into hidden layer hidden_inputs = numpy.dot(self.wih, inputs) # calculate the signals emerging from hidden layer hidden_outputs = self.activation_function(hidden_inputs) # calculate signals into final output layer final_inputs = numpy.dot(self.who, hidden_outputs) # calculate the signals emerging from final output layer final_outputs = self.activation_function(final_inputs) # error is the (target - actual) output_errors = targets - final_outputs # hidden layer error is the output_errors, split by weights, recombined at hidden nodes hidden_errors = numpy.dot(self.who.T, output_errors) # update the weights for the links between the hidden and output layer self.who += self.lr * numpy.dot((output_errors * final_outputs * (1.0 - final_outputs)), numpy.transpose(hidden_outputs)) # update the weights for the links between the input and hidden layers self.wih += self.lr * numpy.dot((hidden_errors * hidden_outputs * (1.0 - hidden_outputs)), numpy.transpose(inputs)) pass # query the network def query(self, inputs_list): # convert inputs list to 2d array # ndmin指定数组最小维度，ndmin=2表示强制将数组转换为2维 inputs = numpy.array(inputs_list, ndmin=2).T # calculate signals into hidden layer hidden_inputs = numpy.dot(self.wih, inputs) # calculate the signals emerging from hidden layer hidden_outputs = self.activation_function(hidden_inputs) # calculate signals into final output layer final_inputs = numpy.dot(self.who, hidden_outputs) # calculate the signals emerging from final output layer final_outputs = self.activation_function(final_inputs) return final_outputs # number of input, hidden and output nodes input_nodes = 784 # 784个输入节点 hidden_nodes = 200 # 100个隐藏节点 output_nodes = 10 # 10个输出节点 # learning_rate is 0.5 learning_rate = 0.1 # create instance of neural network n = neuralNetwork(input_nodes, hidden_nodes, output_nodes, learning_rate) # load the mnist training data CSV file into a list training_data_file = open("mnist_data/mnist_train.csv", 'r') training_data_list = training_data_file.readlines() # 读入文件，将之变为一个列表，以行为单位 training_data_file.close() # train the neural network # epochs is the number of times the training data set is used for training epochs = 5 for e in range(epochs): # go through all records in the training data set for record in training_data_list: # split the record by the ',' commas all_values = record.split(',') # scale and shift the inputs inputs = (numpy.asfarray(all_values[1:]) / 255.0 * 0.99) + 0.01 # 1*784，输入层有784个节点 # create the target output values (all 0.01, except the desired label which is 0.99) targets = numpy.zeros(output_nodes) + 0.01 # all_values[0] is the target label for this record targets[int(all_values[0])] = 0.99 n.train(inputs, targets) pass pass # test the neural network test_data_file = open("mnist_data/mnist_test.csv", 'r') test_data_list = test_data_file.readlines() test_data_file.close() # scorecard for how well the network performs, initially empty scorecard = [] # go through all the records in the test data set for record in test_data_list: # split the record by the ',' commas all_values = record.split(',') # correct answer is first value correct_label = int(all_values[0]) print(correct_label, "correct label") # scale and shift the inputs inputs = (numpy.asfarray(all_values[1:]) / 255.0 * 0.99) + 0.01 # query the network outputs = n.query(inputs) # the index of the highest value correesponds to the label label = numpy.argmax(outputs) # 返回数组中最大索引值 print(label, "network's answer") # append correct or incorrect to list if label == correct_label: # network's answer matches correct answer, add 1 to scorecard scorecard.append(1) else: # network's answer doesn't match correct answer, add 0 to scorecard scorecard.append(0) pass pass # calculate the performance score, the fraction of correct answers scorecard_array = numpy.asarray(scorecard) # 将输入转化为数组 print("performance = ", scorecard_array.sum() / scorecard_array.size)

总结

网络训练中矩阵计算起到重要作用，要特别注意两个矩阵相乘时的矩阵形状sigmoid函数的定义域与值域反向误差传播中计算部分要深入理解，书中的三层网络结构中最后一层输出层在计算式也要使用sigmoid函数在一定程度上多次使用数据集训练网络可以提高识别率