rbfols.m

这是一个用RBF神经网络实现osl的源程序代码

function RBFOLS
SamNum=100;%训练样本数
TestSamNum=101;%测试样本数
SP=0.6;%隐节点扩展常数
ErrorLimit=0.9;  %目标误差

%根据目标函数获得样本输入输出
rand('state',sum(100*clock))
%t=rand(0.1*'state',sum(0.01*clock))%这是一个11*21矩阵
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+')
%figure
%hold on
%grid
plot(TestSamIn,TestSamOut,'k--')
xlabel('Input x');
ylabel('Output y');

[InDim,MaxUnitNum]=size(SamIn);%样本输入维数和最大允许隐节点数
%计算隐节点输出阵
Distance=dist(SamIn',SamIn);
HiddenUnitOut=radbas(Distance/SP);

PosSelected=[];
VectorsSelected=[];
HiddenUnitOutSelected=[];
ErrHistory=[];%用于记录每次增加隐节点后的训练误差

VectorsSelectFrom=HiddenUnitOut;

dd=sum((SamOut.*SamOut)')';
for k=1:MaxUnitNum
    %计算各隐节点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);%用广义逆求广义输出权值
    W2=W2Ex(:,1:k);%得到输出权值
    B2=W2Ex(:,k+1);%得到偏移
    NNOut=W2*HiddenUnitOutSelected+B2;%计算RBF网输出
    SSE=sumsqr(SamOut-NNOut)
    
    %记录每次增加隐节点后的训练误差
    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-')
figure
hold on
grid
[xx,Num]=size(ErrHistory);
plot(1:Num,ErrHistory,'k-')
xlabel('Num')
ylabel('SSE')

k
UnitCenters
W2
B2