Back Propagation后向传播算法 Python实现

后向传播算法用来自动调节神经网络的参数，本次实现代码完全参照Back Propagation的讲解
选取sklearn.datasets的moon数据集的前250个样本进行训练，迭代10000次之后可以得到训练准确率达到87.6%

#!/bin/bash/env python#-*- coding: utf-8__author__ = 'ZhangJin'import numpy as npclass BPNN:    def __init__(self, input_array, output_array, layer_node_count_list, w_step_size=0.02, b_step_size=0.02):        # layers记录每一层的输出,网络是从第0层开始算的        self.layers = []        self.input_array = input_array        self.output_array = output_array        self.layer_node_count_list = layer_node_count_list        self.w_step_size = w_step_size        self.b_step_size = b_step_size        # layer_count是网络的所有层数减1        self.layer_count = len(self.layer_node_count_list) - 1        self.w_dic = {}        #w_dic是一个dictionary，记录每个层的权重（除了输入层，它没有权重和bias)        self.b_dic = {}        # 初始化所有的w和b，        for i in range(1,len(self.layer_node_count_list)):            self.w_dic[i] = 2*(np.random.random((layer_node_count_list[i],layer_node_count_list[i-1]))-0.5)            self.b_dic[i] = 2*(np.random.random((1, layer_node_count_list[i]))-0.5)    def sigmoid(self, x, derivative=False):        if derivative:            return x*(1-x)        else:            return 1/(1+np.exp(-x))    def forward(self):        self.layers = []        self.layers.append(self.input_array)        for i in range(self.layer_count):            z = np.dot(self.layers[i], self.w_dic[i+1].T) + self.b_dic[i+1]            a = self.sigmoid(z)            self.layers.append(a)    def backward(self):        delta_list = []        theta_output = (self.output_array - self.layers[-1]) * self.sigmoid(self.layers[-1],derivative=True)                    #  (self.layers[-1]*(1-self.layers[-1]))        delta_list.append(theta_output)        for i in range(self.layer_count-1, 0, -1):            theta = np.dot(delta_list[-1], self.w_dic[i+1]) * self.sigmoid(self.layers[i],derivative=True)                     # (self.layers[i]*(1-self.layers[i]))            delta_list.append(theta)        delta_list.reverse()        w_change_dic = {}        b_change_dic = {}        N = len(self.input_array)        for i in range(len(delta_list)):            w_change_dic[i+1] = np.dot(delta_list[i].T,self.layers[i]) / float(N) * self.w_step_size            b_change_dic[i+1] = np.sum(delta_list[i],0)/float(N)*self.b_step_size        for i in w_change_dic.keys():            self.w_dic[i] += w_change_dic[i]            self.b_dic[i] += b_change_dic[i]     if __name__ == '__main__':    from sklearn.datasets import make_moons    x, y = make_moons(250, noise = 0.25)    N = 250    yy = np.reshape(y,[N,1])    bpnn = BPNN(x, yy, [2,3,4,1], w_step_size=0.5,b_step_size=0.5)    for i in range(10000):        bpnn.forward()        bpnn.backward()    print bpnn.layers[-1]    cnt = 0    # 计算准确率    for i in range(N):        if np.abs(yy[i] - bpnn.layers[-1][i]) <= 0.5:            cnt += 1    print cnt / float(N)