import numpy as np
import numpy.random
import scipy.special
class NeuralNetwork:
# initialise the neural network
def __init__(self, input_nodes_num, hidden_nodes_num, output_nodes_num, lr):
# 初始化神经元个数,可以直接修改
self.input_nodes = input_nodes_num
self.hidden_nodes = hidden_nodes_num
self.output_nodes = output_nodes_num
self.learning_rate = lr
# 初始化权重值,利用正态分布函数进行随机初始化,均值为0,方差为神经元个数开方
self.w_input_hidden = numpy.random.normal(0.0, pow(self.hidden_nodes, -0.5),
(self.hidden_nodes, self.input_nodes))
self.w_hidden_output = numpy.random.normal(0.0, pow(self.output_nodes, -0.5),
(self.output_nodes, self.hidden_nodes))
# 初始化激活函数,激活函数选用Sigmoid函数,更加平滑,接近自然界的神经元行为模式
# lambda定义了一个匿名函数
self.activation_function = lambda x: scipy.special.expit(x)
pass
# train the neural network
def train(self, inputs_list, targets_list):
# 将训练集和测试集中的数据转化为列向量
inputs = np.array(inputs_list, ndmin=2).T
targets = np.array(targets_list, ndmin=2).T
# 隐藏层的输入为训练集与权重值的点乘,输出为激活函数的输出
hidden_inputs = np.dot(self.w_input_hidden, inputs)
hidden_outputs = self.activation_function(hidden_inputs)
# 输出层的输入为隐藏层的输出,输出为最终结果
final_inputs = np.dot(self.w_hidden_output, hidden_outputs)
final_outputs = self.activation_function(final_inputs)
# 损失函数
output_errors = targets - final_outputs
# 隐藏层的误差为权值矩阵的转置与输出误差的点乘
hidden_errors = np.dot(self.w_hidden_output.T, output_errors)
# 对权值进行更新
self.w_hidden_output += self.learning_rate * np.dot((output_errors *
final_outputs * (1.0 - final_outputs)),
np.transpose(hidden_outputs))
self.w_input_hidden += self.learning_rate * np.dot((hidden_errors *
hidden_outputs * (1.0 - hidden_outputs)),
np.transpose(inputs))
pass
# query the neural network
def query(self, inputs_list):
# 转置将行向量转成列向量,将每组数据更好的分隔开来,方便后续矩阵点乘操作
inputs = np.array(inputs_list, ndmin=2).T
# 加权求和后经过sigmoid函数得到隐藏层输出
hidden_inputs = np.dot(self.w_input_hidden, inputs)
hidden_outputs = self.activation_function(hidden_inputs)
# 加权求和后经过sigmoid函数得到最终输出
final_inputs = np.dot(self.w_hidden_output, hidden_outputs)
final_outputs = self.activation_function(final_inputs)
# 得到输出数据列
return final_outputs
# 初始化各层神经元个数,期中输入神经元个数取决于读入的因变量,而输出神经元个数取决于分类的可能性个数
input_nodes = 784
hidden_nodes = 500
output_nodes = 10
# 学习率,每次调整步幅大小
learning_rate = 0.2
n = NeuralNetwork(input_nodes, hidden_nodes, output_nodes, learning_rate)
# 获取训练集信息
training_data_file = open('data/mnist_train.csv', 'r')
training_data_list = training_data_file.readlines()
training_data_file.close()
for record in training_data_list:
all_values = record.split(',')
inputs = (numpy.asfarray(all_values[1:]) / 255.0 * 0.99) + 0.01
targets = numpy.zeros(output_nodes) + 0.01
targets[int(all_values[0])] = 0.99
n.train(inputs, targets)
pass
print('train successful!')
test_file = open('data/mnist_test.csv', 'r')
test_list = test_file.readlines()
test_file.close()
m = np.size(test_list)
j = 0.0
for record in test_list:
test_values = record.split(',')
np.asfarray(test_values)
results = n.query(np.asfarray(test_values[1:]))
if results[int(test_values[0])] == max(results):
j += 1
pass
print("正确率为;" + str(j/m))