基于聚类的RBF 网设计算法

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1. SamNum = 100; % 总样本数
   
2. TestSamNum = 101; % 测试样本数
   
3. InDim = 1; % 样本输入维数
   
4. ClusterNum = 10; % 隐节点数，即聚类样本数
   
5. Overlap = 1.0; % 隐节点重叠系数
   
6. 
   
7. % 根据目标函数获得样本输入输出
   
8. rand('state',sum(100*clock))
   
9. NoiseVar = 0.1;
   
10. Noise = NoiseVar*randn(1,SamNum);
    
11. SamIn = 8*rand(1,SamNum)-4;
    
12. SamOutNoNoise = 1.1*(1-SamIn+2*SamIn.^2).*exp(-SamIn.^2/2);
    
13. SamOut = SamOutNoNoise + Noise;
    
14. 
    
15. TestSamIn = -4:0.08:4;
    
16. TestSamOut = 1.1*(1-TestSamIn+2*TestSamIn.^2).*exp(-TestSamIn.^2/2);
    
17. 
    
18. figure
    
19. hold on
    
20. grid
    
21. plot(SamIn,SamOut,'k+')
    
22. plot(TestSamIn,TestSamOut,'k--')
    
23. xlabel('Input x');
    
24. ylabel('Output y');
    
25. 
    
26. Centers = SamIn(:,1:ClusterNum);
    
27. 
    
28. NumberInClusters = zeros(ClusterNum,1); % 各类中的样本数，初始化为零
    
29. IndexInClusters = zeros(ClusterNum,SamNum); % 各类所含样本的索引号
    
30. while 1,
    
31. NumberInClusters = zeros(ClusterNum,1); % 各类中的样本数，初始化为零
    
32. IndexInClusters = zeros(ClusterNum,SamNum); % 各类所含样本的索引号
    
33. 
    
34. % 按最小距离原则对所有样本进行分类
    
35. for i = 1:SamNum
    
36. AllDistance = dist(Centers',SamIn(:,i));
    
37. [MinDist,Pos] = min(AllDistance);
    
38. NumberInClusters(Pos) = NumberInClusters(Pos) + 1;
    
39. IndexInClusters(Pos,NumberInClusters(Pos)) = i;
    
40. end
    
41. % 保存旧的聚类中心
    
42. OldCenters = Centers;
    
43. 
    
44. for i = 1:ClusterNum
    
45. Index = IndexInClusters(i,1:NumberInClusters(i));
    
46. Centers(:,i) = mean(SamIn(:,Index)')';
    
47. end
    
48. % 判断新旧聚类中心是否一致，是则结束聚类
    
49. EqualNum = sum(sum(Centers==OldCenters));
    
50. if EqualNum == InDim*ClusterNum,
    
51. break,
    
52. end
    
53. end
    
54. 
    
55. % 计算各隐节点的扩展常数（宽度）
    
56. AllDistances = dist(Centers',Centers); % 计算隐节点数据中心间的距离（矩阵）
    
57. Maximum = max(max(AllDistances)); % 找出其中最大的一个距离
    
58. for i = 1:ClusterNum % 将对角线上的0 替换为较大的值
    
59. AllDistances(i,i) = Maximum+1;
    
60. end
    
61. Spreads = Overlap*min(AllDistances)'; % 以隐节点间的最小距离作为扩展常数
    
62. 
    
63. % 计算各隐节点的输出权值
    
64. Distance = dist(Centers',SamIn); % 计算各样本输入离各数据中心的距离
    
65. SpreadsMat = repmat(Spreads,1,SamNum);
    
66. HiddenUnitOut = radbas(Distance./SpreadsMat); % 计算隐节点输出阵
    
67. HiddenUnitOutEx = [HiddenUnitOut' ones(SamNum,1)]'; % 考虑偏移
    
68. W2Ex = SamOut*pinv(HiddenUnitOutEx); % 求广义输出权值
    
69. W2 = W2Ex(:,1:ClusterNum); % 输出权值
    
70. B2 = W2Ex(:,ClusterNum+1); % 偏移
    
71. 
    
72. % 测试
    
73. TestDistance = dist(Centers',TestSamIn);
    
74. TestSpreadsMat = repmat(Spreads,1,TestSamNum);
    
75. TestHiddenUnitOut = radbas(TestDistance./TestSpreadsMat);
    
76. TestNNOut = W2*TestHiddenUnitOut+B2;
    
77. plot(TestSamIn,TestNNOut,'k-')
    
78. W2
    
79. B2

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