# 神经网络

# 定义神经网络

# python notebook for Make Your Own Neural Network
# code for a 3-layer neural network, and code for learning the MNIST dataset
# (c) Tariq Rashid, 2016
# license is GPLv2
import numpy
# scipy.special for the sigmoid function expit()
import scipy.special
# library for plotting arrays
import matplotlib.pyplot
# ensure the plots are inside this notebook, not an external window
%matplotlib inline

# 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 
        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
        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

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# 创建神经网络

# number of input, hidden and output nodes
input_nodes = 784
hidden_nodes = 200
output_nodes = 10

# learning rate
learning_rate = 0.1

# create instance of neural network
n = neuralNetwork(input_nodes,hidden_nodes,output_nodes, learning_rate)

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# 训练神经网络

# load the mnist training data CSV file into a list
# 将mnist训练数据CSV文件加载到列表中
training_data_file = open("mnist_dataset/mnist_train_100.csv", 'r')
training_data_list = training_data_file.readlines()
training_data_file.close()


# train the neural network
# 训练神经网络

# epochs is the number of times the training data set is used for training
# epochs指的是训练数据集被用于训练的次数
epochs = 5

for e in range(epochs):
    # go through all records in the training data set
    # 遍历训练数据集中的所有记录
    for record in training_data_list:
        # split the record by the ',' commas
        # 用逗号“,”分隔记录
        all_values = record.split(',')
        # scale and shift the inputs
        # 缩放和平移输入
        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)
        # 生成目标输出值（除期望标签为0.99外，其余均为0.01）
        targets = numpy.zeros(output_nodes) + 0.01
        # all_values[0] is the target label for this record
        # all_values[0] 是这条记录的目标标签
        targets[int(all_values[0])] = 0.99
        n.train(inputs, targets)
        pass
    pass

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# 测试训练结果1

# 测试训练结果 1
test_data_file = open("mnist_dataset/mnist_test_10.csv",'r')
test_data_list = test_data_file.readlines()
test_data_file.close()

# 标签是7
all_values = test_data_list[0].split(',')
print(all_values[0])

# n表示的就是神经网络的对象。
n.query((numpy.asfarray(all_values[1:])/255.0 * 0.99) + 0.01)

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输出查询的结果：

array([[0.09415876],
       [0.03253169],
       [0.06191379],
       [0.08234369],
       [0.10396481],
       [0.04755579],
       [0.0190023 ],
       [0.73327761],
       [0.10132217],
       [0.09176148]])

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# 测试训练结果2

# load the mnist test data CSV file into a list
# 将mnist测试数据CSV文件加载到列表中
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
# 遍历测试数据集中的所有记录
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
# 计算表现分数，即正确答案的比例
scorecard_array = numpy.asarray(scorecard)
print ("performance = ", scorecard_array.sum() / scorecard_array.size)

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训练识别率是：

performance =  0.9712