基于MATLAB的径向基网络源程序

%一维输入，一维输出，逼近效果很好！1.基于聚类的RBF网设计算法SamNum=100;%总样本数TestSamNum=101;%测试样本数InDim=1;%样本输入维数ClusterNum=10;%隐节点数，即聚类样本数Overlap=1.0;%隐节点重叠系数%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);figureholdongridplot(SamIn,SamOut,'k+')plot(TestSamIn,TestSamOut,'k--')xlabel('Inputx');ylabel('Outputy');Centers=SamIn(:,1:ClusterNum);NumberInClusters=zeros(ClusterNum,1);%各类中的样本数，初始化为零IndexInClusters=zeros(ClusterNum,SamNum);%各类所含样本的索引号while1,NumberInClusters=zeros(ClusterNum,1);%各类中的样本数，初始化为零IndexInClusters=zeros(ClusterNum,SamNum);%各类所含样本的索引号%按最小距离原则对所有样本进行分类fori=1:SamNumAllDistance=dist(Centers',SamIn(:,i));[MinDist,Pos]=min(AllDistance);NumberInClusters(Pos)=NumberInClusters(Pos)+1;IndexInClusters(Pos,NumberInClusters(Pos))=i;end%保存旧的聚类中心OldCenters=Centers;fori=1:ClusterNumIndex=IndexInClusters(i,1:NumberInClusters(i));Centers(:,i)=mean(SamIn(:,Index)')';end%判断新旧聚类中心是否一致，是则结束聚类EqualNum=sum(sum(Centers==OldCenters));ifEqualNum==InDim*ClusterNum,break,endend%计算各隐节点的扩展常数（宽度）AllDistances=dist(Centers',Centers);%计算隐节点数据中心间的距离（矩阵）Maximum=max(max(AllDistances));%找出其中最大的一个距离fori=1:ClusterNum%将对角线上的0替换为较大的值AllDistances(i,i)=Maximum+1;endSpreads=Overlap*min(AllDistances)';%以隐节点间的最小距离作为扩展常数%计算各隐节点的输出权值Distance=dist(Centers',SamIn);%计算各样本输入离各数据中心的距离SpreadsMat=repmat(Spreads,1,SamNum);HiddenUnitOut=radbas(Distance./SpreadsMat);%计算隐节点输出阵HiddenUnitOutEx=[HiddenUnitOut'ones(SamNum,1)]';%考虑偏移W2Ex=SamOut*pinv(HiddenUnitOutEx);%求广义输出权值W2=W2Ex(:,1:ClusterNum);%输出权值B2=W2Ex(:,ClusterNum+1);%偏移%测试TestDistance=dist(Centers',TestSamIn);TestSpreadsMat=repmat(Spreads,1,TestSamNum);TestHiddenUnitOut=radbas(TestDistance./TestSpreadsMat);TestNNOut=W2*TestHiddenUnitOut+B2;plot(TestSamIn,TestNNOut,'k-')W2B22.基于梯度法的RBF网设计算法SamNum=100;%训练样本数TargetSamNum=101;%测试样本数InDim=1;%样本输入维数UnitNum=10;%隐节点数MaxEpoch=5000;%最大训练次数E0=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))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;TargetIn=-4:0.08:4;TargetOut=1.1*(1-TargetIn+2*TargetIn.^2).*exp(-TargetIn.^2/2);figureholdongridplot(SamIn,SamOut,'k+')plot(TargetIn,TargetOut,'k--')xlabel('Inputx');ylabel('Outputy');Center=8*rand(InDim,UnitNum)-4;SP=0.2*rand(1,UnitNum)+0.1;W=0.2*rand(1,UnitNum)-0.1;lrCent=0.001;%隐节点数据中心学习系数lrSP=0.001;%隐节点扩展常数学习系数lrW=0.001;%隐节点输出权值学习系数ErrHistory=[];%用于记录每次参数调整后的训练误差forepoch=1:MaxEpochAllDist=dist(Center',SamIn);SPMat=repmat(SP',1,SamNum);UnitOut=radbas(AllDist./SPMat);NetOut=W*UnitOut;Error=SamOut-NetOut;%停止学习判断SSE=sumsqr(Error)%记录每次权值调整后的训练误差ErrHistory=[ErrHistorySSE];ifSSEE0,break,endfori=1:UnitNumCentGrad=(SamIn-repmat(Center(:,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)+lrCent*CentGrad;SP(i)=SP(i)+lrSP*SPGrad;W(i)=W(i)+lrW*WGrad;endend%测试TestDistance=dist(Center',TargetIn);TestSpreadsMat=repmat(SP',1,TargetSamNum);TestHiddenUnitOut=radbas(TestDistance./TestSpreadsMat);TestNNOut=W*TestHiddenUnitOut;plot(TargetIn,TestNNOut,'k-')%绘制学习误差曲线figureholdongrid[xx,Num]=size(ErrHistory);plot(1:Num,ErrHistory,'k-');3.基于OLS的RBF网设计算法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))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);figureholdongridplot(SamIn,SamOut,'k+')plot(TestSamIn,TestSamOut,'k--')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=[];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)')';fork=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);ifSelectedNum0,[lin,xxx]=size(Denominator);Denominator(:,PosSelected)=ones(lin,1);endAngle=((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=[PosSelectedpos];%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=[ErrHistorySSE];ifSSEErrorLimit,break,end%作Gram-Schmidt正交化NewVector=VectorsSelectFrom(:,pos);ProjectionLen=NewVector'*VectorsSelectFrom/(NewVector'*NewVector);VectorsSelectFrom=VectorsSelectFrom-NewVect