whk_i.m

魏海坤编著的《神经网络结构设计的理论与方法》 国防工业出版社出版

function main()
AllSamNum=100;
TrainSamNum=75;
TestSamNum=AllSamNum-TrainSamNum;
InDim=1;
UnitNum=12;
MaxEpoch=3000;

% 根据目标函数获得样本输入输出
rand('state',sum(100*clock))
NoiseVar=0.3;
Noise=NoiseVar*randn(1,AllSamNum);
AllSamIn=8*rand(1,AllSamNum)-4;
SamOutNoNoise=1.1*(1-AllSamIn+2*AllSamIn.^2).*exp(-AllSamIn.^2/2);
AllSamOut=SamOutNoNoise+Noise;

TrainSamIn=AllSamIn(:,1:TrainSamNum);
TrainSamOut=AllSamOut(:,1:TrainSamNum);

TestSamIn=AllSamIn(:,TrainSamNum+1:AllSamNum);
TestSamOut=AllSamOut(:,TrainSamNum+1:AllSamNum);

TargetSamIn=-4:0.08:4;
TargetSamOut=1.1*(1-TargetSamIn+2*TargetSamIn.^2).*exp(-TargetSamIn.^2/2);
[xxx,TargetSamNum]=size(TargetSamIn);

clf
hold on
grid
plot(AllSamIn,AllSamOut,'k+')
plot(TargetSamIn,TargetSamOut,'k--')
xlabel('Input x');
ylabel('Output y');
Center=8*rand(InDim,UnitNum)-4;
SP=0.2*rand(1,UnitNum)+0.1;
W=0.2*rand(1,UnitNum)-0.1;

OptimalCenter=Center;
OptimalSP=SP;
OptimalW=W;
OptimalStoppedEpoch=0;
OptimalTestError=0

lrCent=0.001;
lrSP=0.001;
lrW=0.001;
TrainErrHistory=[];
TestErrHistory=[];
TestSSE0=100000;
for epoch=1:MaxEpoch
    AllDist=dist(Center',TrainSamIn);
    SPMat=repmat(SP',1,TrainSamNum);
    UnitOut=radbas(AllDist./SPMat);
    NetOut=W*UnitOut;
    Error=TrainSamOut-NetOut;
    
    % 记录每次权值调整后的训练误差
    SSE=sumsqr(Error)
    TrainErrHistory=[TrainErrHistory SSE];
    
    % 测试误差计算，记录每次权值调整后的测试误差
    TestDistance=dist(Center',TestSamIn);
    TestSpreadsMat=repmat(SP',1,TestSamNum);
    TestHiddenUnitOut=radbas(TestDistance./TestSpreadsMat);
    TestNNOut=W*TestHiddenUnitOut;
    TestError=TestSamOut-TestNNOut;
    TestSSE=sumsqr(TestError);
    TestErrHistory=[TestErrHistory TestSSE];
    
    % 停止学习判断
    if(TestSSE>TestSSE0&OptimalStoppedEpoch==0)
        OptimalCenter=Center;
        OptimalSP=SP;
        OptimalW=W;
        OptimalStoppedEpoch=epoch;
        OptimalTestError=TestSSE;
        
        break;
    end
    
    TestSSE0=TestSSE;
    
    for i=1:UnitNum
        CentGrad=(TrainSamIn-repmat(Center(:,i),1,TrainSamNum))...
                               *(Error.*UnitOut(i,:)*W(i)/(SP(i)^2))';
        SPGrad=AllDist(i,:).^2*(Error.*UnitOut(i,:)*W(i)/(SP(i)^3))';
        WGrad=Error*UnitOut(i,:)';
        
        Center(:,i)=Center(:,i)+lrCent*CentGrad;
        SP(i)=SP(i)+lrSP*SPGrad;
        W(i)=W(i)+lrW*WGrad;
    end
end

% 过拟合结果测试
OverfitTargetDistance=dist(Center',TargetSamIn);
OverfitTargetSpreadsMat=repmat(SP',1,TargetSamNum);
OverfitTargetHiddenUnitOut=radbas(OverfitTargetDistance./OverfitTargetSpreadsMat);
OverfitTargetNNOut=W*OverfitTargetHiddenUnitOut;
plot(TargetSamIn,OverfitTargetNNOut,'b-')
OverfitGeneralizationError=sumsqr(TargetSamIn-OverfitTargetNNOut)

% 最优停止法结果测试
OptimalTargetDistance=dist(OptimalCenter',TargetSamIn);
OptimalTargetSpreadsMat=repmat(OptimalSP',1,TargetSamNum);
OptimalTargetHiddenUnitOut=radbas...
                         (OptimalTargetDistance./OptimalTargetSpreadsMat);
OptimalTargetNNOut=OptimalW*OptimalTargetHiddenUnitOut;
plot(TargetSamIn,OptimalTargetNNOut,'k-')
OptimalStoppedEpoch
OptimalGeneralizationError=sumsqr(TargetSamIn-OptimalTargetNNOut)
OptimalTestError

pause
% 绘制学习误差曲线
figure;
hold on
grid
[xx,Num]=size(TrainErrHistory);
plot(1:Num,TrainErrHistory/TrainSamNum,'k-');
plot(1:Num,TestErrHistory/TestSamNum,'r-');