sflf.m

bp神经网络的经典之一

function main()
InDim=2;
OutDim=3;

figure
colordef(gcf,'white')
echo off
clc
axis([-2,2,-2,2])
axis on
grid
xlabel('Input x');
ylabel('Input y');
line([-1 1],[1 1])
line([1 -1],[1 0])
line([-1 -1],[0 1])
line([-1 1],[-0.5 -0.5])
line([-1 1],[-1.5 -1.5])
line([1 1],[-0.5 -1.5])
line([-1 -1],[-0.5 -1.5])
hold on

SamNum=200;
rand('state',sum(100*clock))
SamIn=(rand(2,SamNum)-0.5)*4;

SamOut=[];
for i=1:SamNum
    Sam=SamIn(:,i);
    x=Sam(1,1);
    y=Sam(2,1);
    if ((x>-1)&(x<1))==1
        if ((y>x/2+1/2)&(y<1))==1
            plot(x,y,'k+')
            class=[0 1 0]';
        elseif ((y<-0.5)&(y>-1.5))==1
            plot(x,y,'ks')
            class=[0 0 1]';
        else
        plot(x,y,'ko')
        class=[1 0 0]';
        end
    else
        plot(x,y,'ko')
        class=[1 0 0]';
    end
    SamOut=[SamOut class];
end

HiddenUnitNum=10;
MaxEpochs=10000;
lr=0.1;
E0=0.01;

W1=0.2*rand(HiddenUnitNum,InDim)-0.1; %输入层到隐层的初始权值
B1=0.2*rand(HiddenUnitNum,1)-0.1;     %隐节点初始偏移
W2=0.2*rand(OutDim,HiddenUnitNum)-0.1;%隐层到输出层的初始权值
B2=0.2*rand(OutDim,1)-0.1;            %输出层初始权值

W1Ex=[W1 B1];                         %输出层到隐层的初始权值扩展
W2Ex=[W2 B2];                         %隐层到输出层的初始权值

SamInEx=[SamIn' ones(SamNum,1)]';     %样本输入扩展
ErrHistory=[];                        %用于记录每次权值调整后的训练误差
for i=1:MaxEpochs
    %正向传播计算网络输出
HiddenOut=logsig(W1Ex*SamInEx);
HiddenOutEx=[HiddenOut' ones(SamNum,1)]';
NetworkOut=logsig(W2Ex*HiddenOutEx);

%停止学习判断
Error=SamOut-NetworkOut;
SSE=sumsqr(Error)

%记录每次权值调整后的训练误差
ErrHistory=[ErrHistory SSE];

if SSE<E0,break,end

%计算反向传播误差
Delta2=Error.*NetworkOut.*(1-NetworkOut);
Delta1=W2'*Delta2.*HiddenOut.*(1-HiddenOut);

%计算权值调节量
dW2Ex=Delta2*HiddenOutEx';
dW1Ex=Delta1*SamInEx';

%权值调整
W1Ex=W1Ex+lr* dW1Ex
W2Ex=W2Ex+lr* dW2Ex;

%分离隐层到输出层的初始权值，以便后面使用
W2=W2Ex(:,1:HiddenUnitNum);

end


W1=W1Ex(:,1:InDim);
B1=W1Ex(:,InDim+1);
W2=W2Ex(:,1:HiddenUnitNum);
B2=W2Ex(:,1+HiddenUnitNum);

%绘制学习误差曲线
figure 
hold on
grid
[xx,Num]=size(ErrHistory);
plot(1:Num,ErrHistory,'k-');

TestSamNum=5000;
TestSamIn=(rand(2,TestSamNum)-0.5)*4;

TestHiddenOut=logsig(W1*TestSamIn+repmat(B1,1,TestSamNum));
TestNetworkOut=logsig(W2*TestHiddenOut+repmat(B2,1,TestSamNum));
[Val,NNClass]=max(TestNetworkOut);

TestTargetOut=[];
for i=1:TestSamNum
    Sam=TestSamIn(:,i);
    x=Sam(1,1);
    y=Sam(2,1);
    if ((x>-1)&(x<1))==1
        if ((y>x/2+1/2)&(y<1))==1
           TestTargetOut=[TestTargetOut 2];
        elseif ((y<-0.5)&(y>-1.5))==1
           TestTargetOut=[TestTargetOut 3];
        else
           TestTargetOut=[TestTargetOut 1];
        end
    else
           TestTargetOut=[TestTargetOut 1];
    end
end

NNC1Flag=abs(NNClass-1)<0.1;
NNC2Flag=abs(NNClass-2)<0.1;
NNC3Flag=abs(NNClass-3)<0.1;

TargetC1Flag=abs(TestTargetOut-1)<0.1;
TargetC2Flag=abs(TestTargetOut-2)<0.1;
TargetC3Flag=abs(TestTargetOut-3)<0.1;

Test_C1_num=sum(NNC1Flag)
Test_C2_num=sum(NNC2Flag)
Test_C3_num=sum(NNC3Flag)

Test_C1_C1=1.0*NNC1Flag*TargetC1Flag'
Test_C1_C2=1.0*NNC1Flag*TargetC2Flag'
Test_C1_C3=1.0*NNC1Flag*TargetC3Flag'

Test_C2_C1=1.0*NNC2Flag*TargetC1Flag'
Test_C2_C2=1.0*NNC2Flag*TargetC2Flag'
Test_C2_C3=1.0*NNC2Flag*TargetC3Flag'

Test_C3_C1=1.0*NNC3Flag*TargetC1Flag'
Test_C3_C2=1.0*NNC3Flag*TargetC2Flag'
Test_C3_C3=1.0*NNC3Flag*TargetC3Flag'

Test_Correct=(Test_C1_C1+Test_C2_C2+Test_C3_C3)/TestSamNum