whk_e.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=100;
TestSamNum=101;
SP=0.6;
ErrorLimit=0.9;

% 根据目标函数获得样本输入输出
rand('state',sum(100*clock))
NoiseVar=0.1;
Noise=NoiseVar*randn(1,SamNum);
SamIn=8*rand(1,SamNum)-4;
SamOutNoNoise=1.1*(1-SamIn+2*SamIn.^2).*exp(SamIn.^2/2);
SamOut=SamOutNoNoise+Noise;

TestSamIn=-4:0.08:4;
TestSamOut=1.1*(1-TestSamIn+2*TestSamIn.^2).*exp(TestSamIn.^2/2);

figure
hold on
grid
plot(SamIn,SamOut,'k+')
plot(TestSamIn,TestSamOut,'k--')
xlabel('Input x');
ylabel('Output y');

[InDim,MaxUnitNum]=size(SamIn);

% 计算隐节电输出阵
Distance=dist(SamIn',SamIn);
HiddenUnitOut=radbas(Distance/SP);

PosSelected=[];
VctorsSelected=[];
HiddenUnitOutSelected=[];
ErrHistory=[];

VectorsSelectFrom=HiddenUnitOut;

dd=sum((SamOut.*SamOut)')';
for k=1:MaxUnitNum
    % 计算各隐节电输出矢量与目标输出矢量的夹角平方值
    PP=sum(VectorsSelectFrom.*VectorsSelectFrom)';
    Denominator=dd*PP';
    [xxx,SelectedNum]=size(PosSelected);
    if SelectedNum>0,
        [lin,xxx]=size(Denominator);
        Denominator(:,PosSelected)=ones(lin,1);
    end
    Angle=((SamOut*VectorsSelectFrom).^2)./Denominator;
    
    % 选择具有最大投影的矢量，得到相应的数据中心
    [value,pos]=max(Angle);
    PosSelected=[PosSelected pos];
    
    % 计算RBF网训练误差
    HiddenUnitOutSelected=[HiddenUnitOutSelected;HiddenUnitOut(pos,:)];
    HiddenUnitOutEx=[HiddenUnitOutSelected;ones(1,SamNum)];
    W2Ex=SamOut*pinv(HiddenUnitOutEx);
    W2=W2Ex(:,1:k);
    B2=W2Ex(:,k+1);
    NNOut=W2*HiddenUnitOutSelected+B2;
    SSE=sumsqr(SamOut-NNOut)
    
    % 记录每次增加隐节电后的训练误差
    ErrHistory=[ErrHistory SSE];
    
    if SSE<ErrorLimit,break,end
    
    % 作Gram-Schmidt正交化
    NewVector=VectorsSelectFrom(:,pos);
    ProjectionLen=NewVector'*VectorsSelectFrom/(NewVector'*NewVector);
    VectorsSelectFrom=VectorsSelectFrom-NewVector*ProjectionLen;
end

UnitCenters=SamIn(PosSelected);

% 测试
TestDistance=dist(UnitCenters',TestSamIn);
TestHiddenUnitOut=radbas(TestDistance/SP);
TestNNOut=W2*TestHiddenUnitOut+B2;
plot(TestSamIn,TestNNOut,'k-')

k
UnitCenters
W2
B2