whk_g.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()
SamNum=15;
TargetSamNum=201;
InDim=1;
UnitNum=15;

NoiseVar=0.4;

% 根据目标函数获得样本输入输出
SamIn=-1+2/SamNum:2/SamNum:1;
SamOutNoNoise=sin(3*(SamIn+0.8).^2);

TargetIn=-1:0.01:1;
TargetOut=sin(3*(TargetIn+0.8).^2);

lr=0.006;
MaxEpoch=1000;
E0=0.01;
InNoiseVar=0.1;

TestNum=1;
tpGradRBF=[lr,MaxEpoch,E0];
tpGradRBFNoiseIn=[lr,MaxEpoch,E0,InNoiseVar];

AllTrainSSENoNoise=[];
AllTestSSENoNoise=[];
AllTrainSSENoNoiseIn=[];
AllTestSSENoNoiseIn=[];
for test=1:TestNum
    % 训练样本输出加噪声
    rand('state'),sum(100*clock))
    Noise=NoiseVar*randn(1,SamNum);
    SamOut=SamOutNoNoise+Noise;
    %产生同样的神经网络参数
    Center=rands(InDim,UnitNum);
    SP=0.2*rand(1,UnitNum)+0.1;
    W=0.1*rands(1,UnitNum);
    %无输入噪声训练
    [NewCenter,NewW,nEWsp,ErrHistory]=RBRGrad(Center,W,SP,SamIn,SamOut,tpGradRBF)
    [xx,TranedEpoch]=size(ErrHistory);
    TrainSSENoNoise=ErrHistory(TranedEpoch);
    AllTrainSSENoNoise=[AllTrainSSENoNoise TrainSSENoNoise];
    % 无输入噪声训练结果测试
   TestNNOutNoNoise=RBF(NewCenter,NewW,NewSP,TargetIn);
   TestSSENoNoise=sumsqr(TargetOut-TestNNOutNoNoise);
   AllTestSSENoNoise=[AllTestSSENoNoise TestSSNoNoise];
   %加输入噪声训练
   [NewCenter,NewW,NewSP,ErrHistory]=RBFGradNoiseIn(Center,W,SP,SamIn,SumOut,tpGradRBFNoiseIn);
   [xx,TrainedEpoch]=size(ErrHistory);
   TrainSSENoiseIn=ErrHistory(TrainedEpoch);
   AllTrainSSNoiseIn=[AllTrainSSNoiseIn TrainSSENoiseIn];
   %加输入噪声训练结果测试
   TestNNOutNoiseIn=RBF(NewCenter,NewW,NewSP,TargetIn);
   TrainSSENoiseIn=sumsqr(TargetOut-TestNNOutNoiseIn);
   AllTestSSENoise=[TestSSENoNoise TrainSSENoideIn TestSSENoiseIn];
   
   [test TrainaSSENoNoise TestSSENoNoise TrainSSENoiseIn TestSSENoiseIn]
end
[mean(AllTrainSSENoise) std(AllTrainSSENoise)]
[mean(AllTestSSENoise) std(AllTestSSENoise)]
[mean(AllTrainSSENoise) std(AllTrainSSENoise)]
[mean(AllTestSSENoise) std(AllTestSSENoise)]

figure
hold on
axis([-1 1 -2 2])
axis on
xlable('Input x');
ylable('Output y');
plot(SamIn,SamOut,'k+')
plot(TargetIn,TargetOut,'k--')
plot(TargetIn,TestNNOutNoNoise,'k-.')
plot(TargetIn,TestNNOutNoNoise,'k-.')
%绘制学习误差曲线
figure
hold on
grid
[xx,Num]=size(ErrHistory);
plot(1:Num,ErrHistory,'k-');

function NNOut=RBF(Center,W,SP,DataIn)
[xxx,DataNum]=size(DataIn);
Distance=dist(Center',DataIn);
SpreadsMat=repmat(SP',1,DataNum);
HiddenUnitOut=radbas(Distance./SpreadsMat);
NNOut=W*HiddenUnitOut;

function [NewCenter,NewCenter,NewW,NewSP,ErrHistory]=RBFGrad(Center,W,SP,...
                                                       SamIn,SamOut,tp)
%(参考附录D)

function [NewCenter,NewCenter,NewW,NewSP,ErrHistory]=RBFGradNoiseIn(Center,W,SP,SamIn,SamOut,tp) 
lr=tp(1);
MaxEpoch=tp(2);
EO=tp(3);
InNoiseVar=tp(4);
[xxx,SamNum]=size(SamIn);
[xxx,UnitNum]=size(Center);
ErrHistory=[];    %用于纪录每次参数调整后的训练误差
for epoch=1:MaxEpoch
    InNoise=InNoiseVar*randn(1,SamNum);
    AllDist=dist(Center',SamIn+InNoise);
    SPMat=repmat(SP',1SamNum);
    UnitOut=radbas(AllDist./SPMat);
    NetOut=W*UnitOut;
    Error=SamOUT-NetOut;
    %停止学习判断
    SSE=sumsqr(Error);
    
    %纪录每次权值调整后的训练误差
    ErrHistory=[ErrHistory SSE];
    
    if SSE<EO,break,end
    
    for i=1:UnitNum
        CentGrad=(SamIn-repmat(Centr(:,i),1,SamNum))...
                               *(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)+lr*CentGrad;
         SP(i)=SP(i)+lr*SPGrad;
         W(i)=W(i)+lr*WGrad;
    end
end
NewCenter=Center
NewW=W;
NewSP=SP;