olsherm.m

上传RBF源程序

clear,clc;
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,'b+')
plot(TestSamIn,TestSamOut,'r--')
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：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 = ((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)];  % 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-')

k
UnitCenters;
W2;
B2;