hermcmp.m

上传RBF源程序

clear,clc;
SamNum = 100;                       % 训练样本数
TestSamNum = 101;                   % 测试样本数

% 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);

clf
hold on
grid
plot(SamIn,SamOut,'k+')
plot(TestSamIn,TestSamOut,'k--')
xlabel('Input x');
ylabel('Output y');

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
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;   
    
    % 重新计算各类的聚类中心
    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                        % 将距离矩阵的对角线上的0替换为较大的值，以免影响计算
    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)]';     % 将偏移纳入输出权值，故隐节点输出阵加一维
W2Ex = SamOut*pinv(HiddenUnitOutEx);                    % 用广义逆求广义输出权值
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-')

UnitNum = 10;                       % 隐节点数
MaxEpoch = 5000;                    % 最大训练次数
E0 = 0.9;                           %目标误差
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',TestSamIn);
TestSpreadsMat = repmat(SP',1,TestSamNum);
TestHiddenUnitOut = radbas(TestDistance./TestSpreadsMat);
TestNNOut = W*TestHiddenUnitOut;
plot(TestSamIn,TestNNOut,'k-')


SP = 0.6;                           % 隐节点扩展常数
ErrorLimit = 0.9;                   % 目标误差
[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：把所有样本输入作为数据中心，计算各样本输入离各数据中心的距离
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 = ((VectorsSelectFrom' * SamOut')' .^ 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)];  % 将偏移纳入输出权值，故隐节点输出阵加一维
    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-')