rbfols.m

基本遗传算法,RBF神经网络算法,BP神经网络算法,一共5个源代码.程序可移植性强.

function main()
%基于OLS(正交最小二乘学习)的RBF网设计算法
tic,
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;

%根据样本目标函数获得样本输入/输出
rand('state',sum(100*clock))  %产生均匀分布的随机矩阵，元素0.0－1.0
NoiseVar=0.1;
Noise=NoiseVar*randn(1,SamNum);  %产生正态分布的随机矩阵
SamIn=8*rand(1,SamNum)-4;
SamOutNoise=1.1*(1-SamIn+2*SamIn.^2).*exp(-SamIn.^2/2);
SamOut=SamOutNoise+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,'r+')
plot(TestSamIn,TestSamOut,'b-')
xlabel('Inputx');
ylabel('Outputy');

[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=[];
HiddenUnitSelected=[];
ErrHistory=[];  %用于记录每次增加隐节点后的训练误差
HiddenUnitOutSelected=[];
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;%1*100矩阵
    
    %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);
   HiddenUnitOutEx=HiddenUnitOutSelected;
   W2Ex=SamOut*pinv(HiddenUnitOutEx);
    W2=W2Ex(:,1:k);
    %B2=W2Ex(:,k+1);
    NNOut=W2*HiddenUnitOutSelected;
    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);
[m,n]=size(UnitCenters);
m
n
%测试
TestDistance=dist(UnitCenters',TestSamIn);
TestHiddenUnitOut=radbas(TestDistance/SP);
TestNNOut=W2*TestHiddenUnitOut;

hold on
plot(TestSamIn,TestNNOut,'k-')
k
UnitCenters
W2

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