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);

figure hold on grid

plot(SamIn,SamOut,'k+')

plot(TestSamIn,TestSamOut,'k--') xlabel('Input x'); ylabel('Output y');

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 while 1,

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 for i = 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;

for i = 1:ClusterNum

Index = 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)); if EqualNum == InDim*ClusterNum, break, end end

% 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 for i = 1:ClusterNum % 将对角线上的0 替换为较大的值 AllDistances(i,i) = Maximum+1; end

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(:,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-') W2 B2

2.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); figure hold on grid

plot(SamIn,SamOut,'k+') plot(TargetIn,TargetOut,'k--') xlabel('Input x'); ylabel('Output y');

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 for epoch = 1:MaxEpoch AllDist = 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 = [ErrHistory SSE]; if SSE

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; end end % 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 figure hold on grid

[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); figure hold on grid

plot(SamIn,SamOut,'k+')

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-') k

UnitCenters W2 B2