BP神经网络PYthon实现（带有”增加充量项“）

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# Back-Propagation Neural Networks

#



import math

import random

import string



random.seed(0)



# calculate a random number where: a <= rand < b

def rand(a, b):

return (b-a)*random.random() + a



# Make a matrix (we could use NumPy to speed this up)

def makeMatrix(I, J, fill=0.0):

m = []

for i in range(I):

m.append([fill]*J)

return m



# our sigmoid function, tanh is a little nicer than the standard 1/(1+e^-x)

#使用双正切函数代替logistic函数

def sigmoid(x):

return math.tanh(x)



# derivative of our sigmoid function, in terms of the output (i.e. y)

# 双正切函数的导数，在求取输出层和隐藏侧的误差项的时候会用到

def dsigmoid(y):

return 1.0 - y**2



class NN:

def __init__(self, ni, nh, no):

# number of input, hidden, and output nodes

# 输入层，隐藏层，输出层的数量，三层网络

self.ni = ni + 1 # +1 for bias node

self.nh = nh

self.no = no



# activations for nodes

self.ai = [1.0]*self.ni

self.ah = [1.0]*self.nh

self.ao = [1.0]*self.no



# create weights

#生成权重矩阵，每一个输入层节点和隐藏层节点都连接

#每一个隐藏层节点和输出层节点链接

#大小：self.ni*self.nh

self.wi = makeMatrix(self.ni, self.nh)

#大小：self.ni*self.nh

self.wo = makeMatrix(self.nh, self.no)

# set them to random vaules

#生成权重，在-0.2-0.2之间

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)



# last change in weights for momentum

#?

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('wrong number of inputs')



# input activations

# 输入的激活函数，就是y=x;

for i in range(self.ni-1):

#self.ai[i] = sigmoid(inputs[i])

self.ai[i] = inputs[i]



# hidden activations

#隐藏层的激活函数,求和然后使用压缩函数

for j in range(self.nh):

sum = 0.0

for i in range(self.ni):

#sum就是《ml》书中的net

sum = sum + self.ai[i] * self.wi[i][j]

self.ah[j] = sigmoid(sum)



# output activations

#输出的激活函数

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[:]



#反向传播算法 targets是样本的正确的输出

def backPropagate(self, targets, N, M):

if len(targets) != self.no:

raise ValueError('wrong number of target values')



# calculate error terms for output

#计算输出层的误差项

output_deltas = [0.0] * self.no

for k in range(self.no):

#计算k-o

error = targets[k]-self.ao[k]

#计算书中公式4.14

output_deltas[k] = dsigmoid(self.ao[k]) * error



# calculate error terms for hidden

#计算隐藏层的误差项，使用《ml》书中的公式4.15

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



# update output weights

# 更新输出层的权重参数

# 这里可以看出，本例使用的是带有“增加冲量项”的BPANN

# 其中，N为学习速率 M为充量项的参数 self.co为冲量项

# N: learning rate

# M: momentum factor

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

#print N*change, M*self.co[j][k]



# update input weights

#更新输入项的权重参数

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



# calculate error

#计算E(w)

error = 0.0

for k in range(len(targets)):

error = error + 0.5*(targets[k]-self.ao[k])**2

return error



#测试函数，用于测试训练效果

def test(self, patterns):

for p in patterns:

print(p[0], '->', self.update(p[0]))



def weights(self):

print('Input weights:')

for i in range(self.ni):

print(self.wi[i])

print()

print('Output weights:')

for j in range(self.nh):

print(self.wo[j])



def train(self, patterns, iterations=1000, N=0.5, M=0.1):

# N: learning rate

# M: momentum factor

for i in range(iterations):

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('error %-.5f' % error)





def demo():

# Teach network XOR function

pat = [

[[0,0], [0]],

[[0,1], [1]],

[[1,0], [1]],

[[1,1], [0]]

]



# create a network with two input, two hidden, and one output nodes

n = NN(2, 2, 1)

# train it with some patterns

n.train(pat)

# test it

n.test(pat)







if __name__ == '__main__':

demo()

输出

>>> ================================ RESTART ================================

>>>

error 0.94250

error 0.04287

error 0.00348

error 0.00164

error 0.00106

error 0.00078

error 0.00125

error 0.00053

error 0.00044

error 0.00038

([0, 0], '->', [0.03668584043139609])

([0, 1], '->', [0.9816625517128087])

([1, 0], '->', [0.9815264813097478])

([1, 1], '->', [-0.03146072993485337])

>>>