zuixiaoercheng2.m

最小二乘法

clc
clear
SamNum=100;          %Training  Sample No.
TestSamNum=101;    %Testing Sample No.
SP=0.6;                    % a fixed spread constant
ErrorLimit=.9;            % goal error

% according to Goal Function to get input and output samples.
rand('state',sum(100*clock))
NoiseVar=0.1;
Noise=NoiseVar*randn(1,SamNum);%Dimension: 1*SamNum
SamIn=8*rand(1,SamNum)-4;
SamOutNoNoise=1.1*(1-SamIn+2*SamIn.^2).*exp(-SamIn.^2/2);
SamOut=SamOutNoNoise+Noise;
%以上是产生的输入输出对应的值
TestSamIn=-4:0.08:4;
TestSamOut=1.1*(1-TestSamIn+2*TestSamIn.^2).*exp(-TestSamIn.^2/2);     % Testing Samples  as a smooth curve. we need to fix to it.
%以上为测试样本的输入输出的对应的值
figure
hold on
grid
plot(SamIn,SamOut,'r+');            % Training Samples have some noise. see the figure.
plot(TestSamIn,TestSamOut,'b--');
xlabel('Input x');
ylabel('Output y');
%以上为训练样本的曲线及测试样本的曲线 
[InDim,MaxUnitNum]=size(SamIn);    %  here the  dimension is 1,and the maximum hidden units is the training sample Number

Distance=dist(SamIn',SamIn);          %hidden layer weights is  SamIn's transpose ??
HiddenUnitOut=radbas(Distance/SP)     % and this is the output of Hidden layer??
%
PosSelected=[];
VectorsSelected=[];
HiddenUnitOutSelected=[];
ErrHistory=[];

VectorsSelectedFrom=HiddenUnitOut;

dd=sum((SamOut.*SamOut)')'
for k=1:MaxUnitNum
    PP=sum(VectorsSelectedFrom.*VectorsSelectedFrom)';
    Denominator=dd*PP';
    [xxx,SelectedNum]=size(PosSelected)
    if SelectedNum>0
        [lin,xxx]=size(Denominator);
        Denominator(:,PosSelected)=ones(lin,1);
    end
    Angle=((SamOut*VectorsSelectedFrom).^2)./Denominator;
    
    [value,pos]=max(Angle);
    PosSelected=[PosSelected pos];
    
    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);
    
    ErrHistory=[ErrHistory SSE];
    
    if SSE<ErrorLimit,break,end
    
    NewVector=VectorsSelectedFrom(:,pos);
    ProjectionLen=NewVector'*VectorsSelectedFrom/(NewVector'*NewVector);
    VectorsSeclectedFrom=VectorsSelectedFrom-NewVector*ProjectionLen;
end

UnitCenters=SamIn(PosSelected);

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