代码如下:
import math import random import string random.seed(0) def rand(a, b): return (b-a)*random.random() + a def makeMatrix(I, J, fill=0.0): m = [] for i in range(I): m.append([fill]*J) return m def sigmoid(x): return math.tanh(x) def dsigmoid(y): return 1.0 - y**2 class neuralNetwork: """三层BP网络""" def __init__(self, ni, nh, no): # 输入层 隐藏层 输出层 self.ni = ni + 1 self.nh = nh self.no = no # 激活神经网络的所有节点(向量) self.ai = [1.0]*self.ni self.ah = [1.0]*self.nh self.ao = [1.0]*self.no # 权重矩阵 self.wi = makeMatrix(self.ni, self.nh) self.wo = makeMatrix(self.nh, self.no) # 设置随机值 for i in range(self.ni): for j in range(self.nh): self.wi[i][j] = rand(-0.2, 0.2) for j in range(self.nh): for k in range(self.no): self.wo[j][k] = rand(-2.0, 2.0) # 最后建立动量因子(矩阵) self.ci = makeMatrix(self.ni, self.nh) self.co = makeMatrix(self.nh, self.no) def update(self, inputs): if len(inputs) != self.ni - 1: raise ValueError('与输入层节点数不符!') # 激活输入层 for i in range(self.ni-1): self.ai[i] = inputs[i] # 激活隐藏层 for j in range(self.nh): sum = 0.0 for i in range(self.ni): sum = sum + self.ai[i] * self.wi[i][j] self.ah[j] = sigmoid(sum) # 激活输出层 for k in range(self.no): sum = 0.0 for j in range(self.nh): sum = sum + self.ah[j] * self.wo[j][k] self.ao[k] = sigmoid(sum) return self.ao[:] def backPropagate(self,targets, N, M): """反向传播""" if len(targets) != self.no: raise ValueError('与输出节点个数不符!') # 计算输出层的误差 output_deltas = [0.0] * self.no for k in range(self.no): error = targets[k] - self.ao[k] output_deltas[k] = dsigmoid(self.ao[k]) * error # 计算隐藏层的误差 hidden_deltas = [0.0] * self.nh for j in range(self.nh): error = 0.0 for k in range(self.no): error = error + output_deltas[k] * self.wo[j][k] hidden_deltas[j] = dsigmoid(self.ah[j]) * error # 更新输出层权重 for j in range(self.nh): for k in range(self.no): change = output_deltas[k] * self.ah[j] self.wo[j][k] = self.wo[j][k] + N*change + M*self.co[j][k] self.co[j][k] = change # 更新输入层权重 for i in range(self.ni): for j in range(self.nh): change = hidden_deltas[j] * self.ai[i] self.wi[i][j] = self.wi[i][j] + N*change + M*self.ci[i][j] self.ci[i][j] = change # 计算误差 error = 0.0 for k in range(len(targets)): error = error + 0.5*(targets[k]-self.ao[k])**2 return error def test(self, patterns): for p in patterns: print(p[0], '->', self.update(p[0])) def weights(self): print('输入层权重:') for i in range(self.ni): print(self.wi[i]) print() print('输出层权重:') for j in range(self.nh): print(self.wo[j]) def train(self, patterns, epoch=10000, N=0.5, M=0.1): # N:学习速率(learnning rate) # M:动量因子(momentum factor) for i in range(epoch): error = 0.0 for p in patterns: inputs = p[0] targets = p[1] self.update(inputs) error = error + self.backPropagate(targets, N, M) if i % 100 == 0: print('误差 %-.5f' % error) def demo(): pat = [ [[0, 0], [0]], [[0, 1], [1]], [[1, 0], [1]], [[1, 1], [0]] ] n = neuralNetwork(2, 2, 1) n.train(pat) n.test(pat) n.weights() if __name__ == '__main__': demo()