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));
= 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 = '; % 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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