BP神经网络PYthon实现（带有”增加充量项“）

# Back-Propagation Neural Networks# import mathimport randomimport stringrandom.seed(0)# calculate a random number where:  a <= rand < bdef 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**2class 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])
>>>