基于MATLAB的径向基网络源程序Word文档格式.docx
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0.08:
4;
TestSamOut=1.1*(1-TestSamIn+2*TestSamIn.^2).*exp(-TestSamIn.^2/2);
figure
holdon
grid
plot(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,
%按最小距离原则对所有样本进行分类
fori=1:
SamNum
AllDistance=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;
ClusterNum
Index=IndexInClusters(i,1:
NumberInClusters(i));
Centers(:
i)=mean(SamIn(:
Index)'
)'
;
%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,
%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
ClusterNum%将对角线上的0替换为较大的值
AllDistances(i,i)=Maximum+1;
Spreads=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(:
%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-'
W2
B2
2.基于梯度法的RBF网设计算法
%训练样本数
TargetSamNum=101;
UnitNum=10;
%隐节点数
MaxEpoch=5000;
%最大训练次数
E0=0.9;
%目标误差
TargetIn=-4:
TargetOut=1.1*(1-TargetIn+2*TargetIn.^2).*exp(-TargetIn.^2/2);
plot(TargetIn,TargetOut,'
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:
MaxEpoch
AllDist=dist(Center'
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];
ifSSE<
E0,break,end
UnitNum
CentGrad=(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;
TestDistance=dist(Center'
TargetIn);
TestSpreadsMat=repmat(SP'
1,TargetSamNum);
TestNNOut=W*TestHiddenUnitOut;
plot(TargetIn,TestNNOut,'
%绘制学习误差曲线
[xx,Num]=size(ErrHistory);
plot(1:
Num,ErrHistory,'
3.基于OLS的RBF网设计算法
SP=0.6;
%隐节点扩展常数
ErrorLimit=0.9;
[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'
HiddenUnitOut=radbas(Distance/SP);
PosSelected=[];
VectorsSelected=[];
HiddenUnitOutSelected=[];
%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);
ifSelectedNum>
0,
[lin,xxx]=size(Denominator);
Denominator(:
PosSelected)=ones(lin,1);
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=[PosSelectedpos];
%计算RBF网训练误差
HiddenUnitOutSelected=[HiddenUnitOutSelected;
HiddenUnitOut(pos,:
)];
HiddenUnitOutEx=[HiddenUnitOutSelected;
ones(1,SamNum)];
%用广义逆求广义输出权值
k);
%得到输出权值
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
ifSSE<
ErrorLimit,break,end
%作Gram-Schmidt正交化
NewVector=VectorsSelectFrom(:
pos);
ProjectionLen=NewVector'
*VectorsSelectFrom/(NewVector'
*NewVector);
VectorsSelectFrom=VectorsSelectFrom-NewVector*ProjectionLen;
UnitCenters=SamIn(PosSelected);
%%%%%%%%%%%
TestDistance=dist(UnitCenters'
%%%%%%%%
TestHiddenUnitOut=radbas(TestDistance/SP);
k
UnitCenters