bp_xor.m

利用三层BP人工神经网络解决异或问题（XOR）用matlab编程实现

clear;clc;
X=[  0     0
     0     1
     1     0
     1     1];%input sample set,each row is a sample vector
T=[ 0;
    1;
    1;
    0];%each row is a output expectation vector
 
[Num_sample,Num_in]=size(X);%Num_sample is the number of samples
                            %Num_in is the number of elements in samples
Num_out=length(T(1,:)); %Num_out is the number of output neurons
Num_hid=2; 

W12=rand(Num_in,Num_hid);
W23=rand(Num_hid,Num_out);

eta=0.7;%eta is learning rate
alpha=1;
E=0;
epsilon=0.166; %0.166 or 0.008

p=1;n=1;	%n is the number of iteration       
while(p<=Num_sample)
    Y1=X(p,:);%训练样本输入，也即第一层的输出
    t=T(p,:);%对应的最后一层的期望输出值
%前向计算
    %第2层（即第一隐层）
    for i=1:Num_hid   %第2层（即第一隐层）中的神经元个数
        V2(i)=Y1*W12(:,i);
        Y2(i)=sigmoid(V2(i));   %计算隐层各个神经元的输出
        %deriv2(i)=Y2(i)*(1-Y2(i));
    end
    %第3层（即输出层）
    for i=1:Num_out
        V3(i)=Y2*W23(:,i);
        Y3(i)=sigmoid(V3(i));   %计算输出层各个神经元的输出
        %deriv3(i)=Y3(i)*(1-Y3(i));
    end
    %误差计算
    e=t-Y3;
    E=E+sum(e.^2)/2;
    if(p==4)    %p=4，表示一个训练周期结束
       % X=[X(2,:);X(4,:);X(1,:);X(3,:)];
       % T=[T(2,:);T(4,:);T(1,:);T(3,:)];
        if(E>epsilon)   %判断终止条件
            p=0;
            E=0;
        end
    end
    
%Error back propagation
    %第3层（输出层）权值调整
    for i=1:Num_out %第i个输出层神经元
        %delta3(i)=e(i)*deriv3(i);
        delta3(i)=e(i)*Y3(i)*(1-Y3(i));
        for j=1:Num_hid %第j个隐层神经元
            W23(j,i)=alpha*W23(j,i)+eta*delta3(i)*Y2(j);
        end
    end    
    %第2层（隐层）权值调整
    for i=1:Num_hid
        %delta2(i)=W23(i,:)*delta3'*deriv2(i);
        delta2(i)=W23(i,:)*delta3'*Y2(i)*(1-Y2(i));
        for j=1:Num_in
            W12(j,i)=alpha*W12(j,i)+eta*delta2(i)*Y1(j);
        end
    end
    
    p=p+1;  %go to the next paired-sample
    n=n+1;  %number of iteration
    if(n>100000)
        error('Maximum Number of Iteration')
        break
    end
end