Python神经网络编程 第二章 使用Python进行DIY
使用神经网络识别手写数字:
import numpy # scipy.special for the sigmoid function expit(),即S函数 import scipy.special # library for plotting arrays import matplotlib.pyplot # ensure the plots are inside this notebook, not an external window %matplotlib inline // 在notebook上绘图,而不是独立窗口 # 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 # weights 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 # numpy.random.normal(loc,scale,size) loc:概率分布的均值;scale:概率分布的方差;size:输出的shape self.wih = numpy.random.normal(0.0, pow(self.inodes, -0.5), (self.hnodes, self.inodes)) self.who = numpy.random.normal(0.0, pow(self.hnodes, -0.5), (self.onodes, self.hnodes)) # learning rate self.lr = learningrate # activation function is the sigmoid function # 使用lambda创建的函数是没有名字的 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) # output layer 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 layers 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 neural network def query(self, inputs_list): # convert inputs list to 2d array 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 # 选择784个输入节点是28*28的结果,即组成手写数字图像的像素个数 input_nodes = 784 # 选择使用100个隐藏层不是通过使用科学的方法得到的。通过选择使用比输入节点的数量小的值,强制网络尝试总结输入的主要特点。 # 但是,如果选择太少的隐藏层节点,会限制网络的能力,使网络难以找到足够的特征或模式。 # 同时,还要考虑到输出层节点数10。 # 这里应该强调一点。对于一个问题,应该选择多少个隐藏层节点,并不存在一个最佳方法。同时,我们也没有最佳方法选择需要几层隐藏层。 # 就目前而言,最好的办法是进行实验,直到找到适合你要解决的问题的一个数字。 hidden_nodes = 200 output_nodes = 10 # learning rate,需要多次尝试,0.2是最佳值 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_dataset/mnist_train.csv", 'r') training_data_list = training_data_file.readlines() training_data_file.close() # train the neural network # epochs is the number of times the training data set is used for training # 就像调整学习率一样,需要使用几个不同的世代进行实验并绘图,以可视化这些效果。直觉告诉我们,所做的训练越多,所得到的的性能越好。 # 但太多的训练实际上会过犹不及,这是由于网络过度拟合训练数据。 # 在大约5或7个世代时,有一个甜蜜点。在此之后,性能会下降,这可能是过度拟合的效果。 # 性能在6个世代的情况下下降,这可能是运行中出了问题,导致网络在梯度下降过程中被卡在了一个局部的最小值中。 # 事实上,由于没有对每个数据点进行多次实验,无法减小随机过程的影响。 # 神经网络的学习过程其核心是随机过程,有时候工作得不错,有时候很糟。 # 另一个可能的原因是,在较大数目的世代情况下,学习率可能设置过高了。在更多世代的情况下,减小学习率确实能够得到更好的性能。 # 如果打算使用更长的时间(多个世代)探索梯度下降,那么可以采用较短的步长(学习率),总体上可以找到更好的路径。 # 要正确、科学地选择这些参数,必须为每个学习率和世代组合进行多次实验,尽量减少在梯度下降过程中随机性的影响。 # 还可尝试不同的隐藏层节点数量,不同的激活函数。 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 # 输入值需要避免0,输出值需要避免1 inputs = (numpy.asfarray(all_values[1:]) / 255.0 * 0.99) + 0.01 # 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 # load the mnist test data CSV file into a list test_data_file = open("mnist_dataset/mnist_test.csv", 'r') test_data_list = test_data_file.readlines() test_data_file.close() # test the neural network # 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]) # 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 corresponds to the label label = numpy.argmax(outputs) # 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) print ("performance = ", scorecard_array.sum() / scorecard_array.size) # performance = 0.9712