%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);figurehold ongridplot(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: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;for i = 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));if EqualNum == 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for i = 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); figurehold ongridplot(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: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 = [ErrHistory SSE];if SSE<E0, break, endfor i = 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figurehold ongrid[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); figurehold ongridplot(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);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 = [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;endUnitCenters = SamIn(PosSelected);%%%%%%%%%%%% 测试TestDistance = dist(UnitCenters',TestSamIn);%%%%%%%% TestHiddenUnitOut = radbas(TestDistance/SP);TestNNOut = W2*TestHiddenUnitOut+B2;plot(TestSamIn,TestNNOut,'k-')kUnitCentersW2B2。