3个径向基网络的matlab源程序

ken1983414

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

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

复制代码

2.基于梯度法的RBF 网设计算法

1. SamNum = 100; % 训练样本数
   
2. TargetSamNum = 101; % 测试样本数
   
3. InDim = 1; % 样本输入维数
   
4. UnitNum = 10; % 隐节点数
   
5. MaxEpoch = 5000; % 最大训练次数
   
6. E0 = 0.9; % 目标误差
   
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. TargetIn = -4:0.08:4;
    
15. TargetOut = 1.1*(1-TargetIn+2*TargetIn.^2).*exp(-TargetIn.^2/2);
    
16. figure
    
17. hold on
    
18. grid
    
19. plot(SamIn,SamOut,'k+')
    
20. plot(TargetIn,TargetOut,'k--')
    
21. xlabel('Input x');
    
22. ylabel('Output y');
    
23. Center = 8*rand(InDim,UnitNum)-4;
    
24. SP = 0.2*rand(1,UnitNum)+0.1;
    
25. W = 0.2*rand(1,UnitNum)-0.1;
    
26. lrCent = 0.001; % 隐节点数据中心学习系数
    
27. lrSP = 0.001; % 隐节点扩展常数学习系数
    
28. lrW = 0.001; % 隐节点输出权值学习系数
    
29. ErrHistory = []; % 用于记录每次参数调整后的训练误差
    
30. for epoch = 1:MaxEpoch
    
31. AllDist = dist(Center',SamIn);
    
32. SPMat = repmat(SP',1,SamNum);
    
33. UnitOut = radbas(AllDist./SPMat);
    
34. NetOut = W*UnitOut;
    
35. Error = SamOut-NetOut;
    
36. %停止学习判断
    
37. SSE = sumsqr(Error)
    
38. % 记录每次权值调整后的训练误差
    
39. ErrHistory = [ErrHistory SSE];
    
40. if SSE<E0, break, end
    
41. for i = 1:UnitNum
    
42. CentGrad = (SamIn-repmat(Center(:,i),1,SamNum))...
    
43. *(Error.*UnitOut(i,*W(i)/(SP(i)^2))';
    
44. SPGrad = AllDist(i,.^2*(Error.*UnitOut(i,*W(i)/(SP(i)^3))';
    
45. WGrad = Error*UnitOut(i,';
    
46. Center(:,i) = Center(:,i) + lrCent*CentGrad;
    
47. SP(i) = SP(i) + lrSP*SPGrad;
    
48. W(i) = W(i) + lrW*WGrad;
    
49. end
    
50. end
    
51. % 测试
    
52. TestDistance = dist(Center',TargetIn);
    
53. TestSpreadsMat = repmat(SP',1,TargetSamNum);
    
54. TestHiddenUnitOut = radbas(TestDistance./TestSpreadsMat);
    
55. TestNNOut = W*TestHiddenUnitOut;
    
56. plot(TargetIn,TestNNOut,'k-')
    
57. % 绘制学习误差曲线
    
58. figure
    
59. hold on
    
60. grid
    
61. [xx,Num] = size(ErrHistory);
    
62. plot(1:Num,ErrHistory,'k-');

复制代码

3.基于OLS 的RBF 网设计算法

1. SamNum = 100; % 训练样本数
   
2. TestSamNum = 101; % 测试样本数
   
3. SP = 0.6; % 隐节点扩展常数
   
4. ErrorLimit = 0.9; % 目标误差
   
5. % 根据目标函数获得样本输入输出
   
6. rand('state',sum(100*clock))
   
7. NoiseVar = 0.1;
   
8. Noise = NoiseVar*randn(1,SamNum);
   
9. SamIn = 8*rand(1,SamNum)-4;
   
10. SamOutNoNoise = 1.1*(1-SamIn+2*SamIn.^2).*exp(-SamIn.^2/2);
    
11. SamOut = SamOutNoNoise + Noise;
    
12. TestSamIn = -4:0.08:4;
    
13. TestSamOut = 1.1*(1-TestSamIn+2*TestSamIn.^2).*exp(-TestSamIn.^2/2);
    
14. figure
    
15. hold on
    
16. grid
    
17. plot(SamIn,SamOut,'k+')
    
18. plot(TestSamIn,TestSamOut,'k--')
    
19. xlabel('Input x');
    
20. ylabel('Output y');
    
21. [InDim,MaxUnitNum] = size(SamIn); % 样本输入维数和最大允许隐节点数
    
22. % 计算隐节点输出阵
    
23. Distance = dist(SamIn',SamIn);
    
24. HiddenUnitOut = radbas(Distance/SP);
    
25. PosSelected = [];
    
26. VectorsSelected = [];
    
27. HiddenUnitOutSelected = [];
    
28. ErrHistory = []; % 用于记录每次增加隐节点后的训练误差
    
29. VectorsSelectFrom = HiddenUnitOut;
    
30. dd = sum((SamOut.*SamOut)')';
    
31. for k = 1 : MaxUnitNum
    
32. % 计算各隐节点输出矢量与目标输出矢量的夹角平方值
    
33. PP = sum(VectorsSelectFrom.*VectorsSelectFrom)';
    
34. Denominator = dd * PP';
    
35. [xxx,SelectedNum] = size(PosSelected);
    
36. if SelectedNum>0,
    
37. [lin,xxx] = size(Denominator);
    
38. Denominator(:,PosSelected) = ones(lin,1);
    
39. end
    
40. Angle = ((SamOut*VectorsSelectFrom) .^ 2) ./ Denominator;
    
41. % 选择具有最大投影的矢量，得到相应的数据中心
    
42. [value,pos] = max(Angle);
    
43. PosSelected = [PosSelected pos];
    
44. % 计算RBF 网训练误差
    
45. HiddenUnitOutSelected = [HiddenUnitOutSelected; HiddenUnitOut(pos,];
    
46. HiddenUnitOutEx = [HiddenUnitOutSelected; ones(1,SamNum)];
    
47. W2Ex = SamOut*pinv(HiddenUnitOutEx); % 用广义逆求广义输出权值
    
48. W2 = W2Ex(:,1:k); % 得到输出权值
    
49. B2 = W2Ex(:,k+1); % 得到偏移
    
50. NNOut = W2*HiddenUnitOutSelected+B2; % 计算RBF 网输出
    
51. SSE = sumsqr(SamOut-NNOut)
    
52. % 记录每次增加隐节点后的训练误差
    
53. ErrHistory = [ErrHistory SSE];
    
54. if SSE < ErrorLimit, break, end
    
55. % 作Gram-Schmidt 正交化
    
56. NewVector = VectorsSelectFrom(:,pos);
    
57. ProjectionLen = NewVector' * VectorsSelectFrom / (NewVector'*NewVector);
    
58. VectorsSelectFrom = VectorsSelectFrom - NewVector * ProjectionLen;
    
59. end
    
60. UnitCenters = SamIn(PosSelected);%%%%%%%%%%%
    
61. % 测试
    
62. TestDistance = dist(UnitCenters',TestSamIn);%%%%%%%%
    
63. TestHiddenUnitOut = radbas(TestDistance/SP);
    
64. TestNNOut = W2*TestHiddenUnitOut+B2;
    
65. plot(TestSamIn,TestNNOut,'k-')
    
66. k
    
67. UnitCenters
    
68. W2
    
69. B2

复制代码

[ 本帖最后由 suffer 于 2006-11-29 09:27 编辑 ]

wateropt

有没有RBF预测的程序？

风融血

好东东，谢谢楼主！

receive

太好了，kiss~~~~~~~

adiko

学习~~

shandazhanglei

谢谢了！ ！

西门牛