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3个径向基网络的matlab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
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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<E0, break, end
- for i = 1: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;
- 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-');
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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
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[ 本帖最后由 suffer 于 2006-11-29 09:27 编辑 ] |
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