Python神经网络编程 第二章 使用Python进行DIY

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