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自组织神经网络SOM原理——结合例子MATLAB实现

分类: 文章 • 2025-02-04 22:07:04

  本文主要内容为SOM神经网络原理的介绍，并结合实例给出相应的MATLAB代码实现，方便初学者接触学习，本人才疏学浅，如有纰漏，还望各路大神积极指点。

一、SOM神经网络介绍

     自组织映射神经网络， 即Self Organizing Maps (SOM)， 可以对数据进行无监督学习聚类。它的思想很简单，本质上是一种只有输入层--隐藏层的神经网络。隐藏层中的一个节点代表一个需要聚成的类。训练时采用“竞争学习”的方式，每个输入的样例在隐藏层中找到一个和它最匹配的节点，称为它的**节点，也叫“winning neuron”。 紧接着用随机梯度下降法更新**节点的参数。同时，和**节点临近的点也根据它们距离**节点的远近而适当地更新参数。

      所以，SOM的一个特点是，隐藏层的节点是有拓扑关系的。这个拓扑关系需要我们确定，如果想要一维的模型，那么隐藏节点依次连成一条线；如果想要二维的拓扑关系，那么就行成一个平面，如下图所示（也叫Kohonen Network）：

自组织神经网络SOM原理——结合例子MATLAB实现

      既然隐藏层是有拓扑关系的，所以我们也可以说，SOM可以把任意维度的输入离散化到一维或者二维(更高维度的不常见)的离散空间上。 Computation layer里面的节点与Input layer的节点是全连接的。

拓扑关系确定后，开始计算过程，大体分成几个部分：

1） 初始化：每个节点随机初始化自己的参数。每个节点的参数个数与Input的维度相同。

2）对于每一个输入数据，找到与它最相配的节点。假设输入时D维的， 即 X={x_i, i=1,...,D}，那么判别函数可以为欧几里得距离：

自组织神经网络SOM原理——结合例子MATLAB实现

3) 找到**节点I(x)之后，我们也希望更新和它临近的节点。令S_ij表示节点i和j之间的距离，对于I(x)临近的节点，分配给它们一个更新权重：

自组织神经网络SOM原理——结合例子MATLAB实现

简单地说，临近的节点根据距离的远近，更新程度要打折扣。

4）接着就是更新节点的参数了。按照梯度下降法更新：

自组织神经网络SOM原理——结合例子MATLAB实现

迭代，直到收敛。



二、问题描述

用26个英文字母作为SOM输入样本。每个字符对应一个5维向量，各字符与向量的关系如表4-2所示。由表4-2可以看出，代表A、B、C、D、E的各向量中有4个分量相同，即，因此，A、B、C、D、E应归为一类；代表F、G、H、I、J的向量中有3个分量相同，同理也应归为一类；依此类推。这样就可以由表4-2中输入向量的相似关系，将对应的字符标在图4-8所示的树形结构图中。用SOM网络对其他进行聚类分析。

自组织神经网络SOM原理——结合例子MATLAB实现

自组织神经网络SOM原理——结合例子MATLAB实现


三、MATLAB代码实现

SOM_mian.m

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  1. %%% 神经网络之自组织网络SOM练习  
  2. %%%作者：xd.wp  
  3. %%%时间：2016.10.02 19：16  
  4. %% 程序说明：  
  5. %%%          1、本程序中，输出层为二维平面，  
  6. %%%          2、几何邻域确定及调整权值采用exp(-distant^2/delta^2)函数  
  7. %%%          3、样本维数为5，输出层结点为70  
  8. %%%          4、输入数据，归一化为单位向量  
  9. clear all;  
  10. clc;  
  11. %% 网络初始化及相应参数初始化  
  12. %加载数据并归一化  
  13. [train_data,train_label]=SOM_data_process();  
  14. data_num=size(train_data,2);  
  15.   
  16. %权值初始化  
  17. % weight_temp=ones(5,70)/1000;  
  18. weight_temp=rand(5,70)/1000;  
  19.   
  20. %结点个数  
  21. node_num=size(weight_temp,2);  
  22.   
  23. %权值归一化  
  24. for i=1:node_num  
  25.     weight(:,i)=weight_temp(:,i)/max(weight_temp(:,i));      
  26. end  
  27.   
  28. %邻域函数参数  
  29. delta=2;  
  30.   
  31. %调整步幅  
  32. alpha=0.6;  
  33. %% Kohonen算法学习过程  
  34. for t=4:-1:1                                    %%总体迭代次数  
  35.     index_active=ones(1,node_num);              %%结点活跃标志  
  36.     for n=1:data_num                            %%每个样本的输入  
  37.         % 竞争部分，根据最小距离确定获胜神经元  
  38.         [j_min]=SOM_compare(weight,train_data(:,n),node_num,index_active);  
  39.           
  40.         %去**，确保数据结点1对1映射  
  41.         index_active(1,j_min)=0;  
  42.           
  43.         %为后续绘图部分服务  
  44.         index_plot(1,n)=j_min;  
  45.         [x,y]=line_to_array(j_min);  
  46.         fprintf('坐标[%d,%d]处为字符%s \n',x,y,train_label(1,n));  
  47.           
  48.         % 学习部分网络权值调整  
  49.         st=num2str(t-1);  
  50.         switch   st  
  51.             case '3'  
  52.                 [weight]=SOM_neighb3(weight,train_data(:,n),j_min,delta,alpha);  
  53.             case '2'  
  54.                 [weight]=SOM_neighb2(weight,train_data(:,n),j_min,delta,alpha);  
  55.             case '1'  
  56.                 [weight]=SOM_neighb1(weight,train_data(:,n),j_min,delta,alpha);  
  57.             otherwise  
  58.                 [weight]=SOM_neighb0(weight,train_data(:,n),j_min,alpha);  
  59.         end  
  60.           
  61.     end  
  62. end  
  63. %% 绘制结点分布图像  
  64. figure(1);  
  65. for n=1:data_num  
  66.     [x,y]=line_to_array(index_plot(1,n));  
  67.     axis([0,12,0,12]);  
  68.     text(x,y,'*');  
  69.     text(x+0.2,y+0.2,train_label(1,n));  
  70.     hold on;  
  71. end  
SOM_data_process.m

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  1. function [train_data,train_label]=SOM_data_process()  
  2. train_data=[1 0 0 0 0;  
  3.             2 0 0 0 0;  
  4.             3 0 0 0 0;  
  5.             4 0 0 0 0;  
  6.             5 0 0 0 0;  
  7.             3 1 0 0 0;  
  8.             3 2 0 0 0;  
  9.             3 3 0 0 0;  
  10.             3 4 0 0 0;  
  11.             3 5 0 0 0;  
  12.             3 3 1 0 0;  
  13.             3 3 2 0 0;  
  14.             3 3 3 0 0;  
  15.             3 3 4 0 0;  
  16.             3 3 5 0 0;  
  17.             3 3 3 1 0;  
  18.             3 3 3 2 0;  
  19.             3 3 3 3 0;  
  20.             3 3 3 4 0;  
  21.             3 3 3 5 0;  
  22.             3 3 3 3 1;  
  23.             3 3 3 3 2;  
  24.             3 3 3 3 3;  
  25.             3 3 3 3 4;  
  26.             3 3 3 3 5;  
  27.             3 3 3 3 6];  
  28. train_label=['A','B','C','D','E','F','G','H','I','J','K','L','M','N','O','P','Q','R','S','T','U','V','W','X','Y','Z','1','2','3','4','5','6'];  
  29. train_data=train_data';  
  30. length=size(train_data,2);  
  31. for i=1:length  
  32.      train_data(:,i)=train_data(:,i)/sqrt(sum(train_data(:,i).*train_data(:,i)));  
  33. % train_data(:,i)=train_data(:,i)/max(train_data(:,i));  
  34. end  
  35. end  

SOM_compare.m

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  1. function [j_min]=SOM_compare(weight,train_data_active,node_num,index_active)  
  2. for j=1:node_num  
  3.     distant(j,1)=sum((weight(:,j)-train_data_active).^2);  
  4. end  
  5. [~,j_min]=min(distant);  
  6. while(index_active(1,j_min)==0)  
  7.     distant(j_min,1)=10000000;  
  8.     [~,j_min]=min(distant);  
  9. end  
  10.   
  11. end  

SOM_neighb3.m
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  1. function [weight]=SOM_neighb3(weight,train_data_active,j_min,delta,alpha)  
  2.   
  3. %% 权值调整幅度分布  
  4. %                          -0.2  
  5. %                           0.2  
  6. %                           0.6  
  7. %        -0.2   0.2   0.6    1    0.6   0.2   -0.2  
  8. %                           0.6  
  9. %                           0.2  
  10. %                          -0.2  
  11. % 单位距离转化比例为0.4  
  12. %% 坐标转换  
  13. [x,y]=line_to_array(j_min);  
  14. % 将1*70向量中的坐标转化为7*10矩阵中的坐标  
  15. %    1   8    ···  
  16. %    7   14   ···  
  17.   
  18. %% 权值调整过程  
  19. %结点靠上边情况  
  20. if (x<=3)  
  21.     for m=1:1:x+3  
  22.         if (y<=3)          %结点靠左边  
  23.             for n=1:1:y+3  
  24.                 distant=sqrt((x-m)^2+(y-n)^2);  
  25.                 weight(:,(n-1)*7+m)=weight(:,(n-1)*7+m)-alpha*exp(-distant^2/delta^2)*(weight(:,(n-1)*7+m)-train_data_active);  
  26.             end  
  27.         elseif (y>=8)      %结点靠右边  
  28.             for n=y-3:1:10  
  29.                 distant=sqrt((x-m)^2+(y-n)^2);  
  30.                 weight(:,(n-1)*7+m)=weight(:,(n-1)*7+m)-alpha*exp(-distant^2/delta^2)*(weight(:,(n-1)*7+m)-train_data_active);  
  31.             end  
  32.         else  
  33.             for n=y-3:1:y+3  
  34.                 distant=sqrt((x-m)^2+(y-n)^2);  
  35.                 weight(:,(n-1)*7+m)=weight(:,(n-1)*7+m)-alpha*exp(-distant^2/delta^2)*(weight(:,(n-1)*7+m)-train_data_active);  
  36.             end  
  37.         end  
  38.     end  
  39.     %结点靠下边情况  
  40. elseif (x>=5)  
  41.     for m=x-3:1:7  
  42.          if (y<=3)          %结点靠左边  
  43.             for n=1:1:y+3  
  44.                 distant=sqrt((x-m)^2+(y-n)^2);  
  45.                 weight(:,(n-1)*7+m)=weight(:,(n-1)*7+m)-alpha*exp(-distant^2/delta^2)*(weight(:,(n-1)*7+m)-train_data_active);  
  46.             end  
  47.         elseif (y>=8)      %结点靠右边  
  48.             for n=y-3:1:10  
  49.                 distant=sqrt((x-m)^2+(y-n)^2);  
  50.                 weight(:,(n-1)*7+m)=weight(:,(n-1)*7+m)-alpha*exp(-distant^2/delta^2)*(weight(:,(n-1)*7+m)-train_data_active);  
  51.             end  
  52.         else  
  53.             for n=y-3:1:y+3  
  54.                 distant=sqrt((x-m)^2+(y-n)^2);  
  55.                 weight(:,(n-1)*7+m)=weight(:,(n-1)*7+m)-alpha*exp(-distant^2/delta^2)*(weight(:,(n-1)*7+m)-train_data_active);  
  56.             end  
  57.         end  
  58.     end  
  59.     %结点正好在中间  
  60. else  
  61.     for m=1:7  
  62.          if (y<=3)          %结点靠左边  
  63.             for n=1:1:y+3  
  64.                 distant=sqrt((x-m)^2+(y-n)^2);  
  65.                 weight(:,(n-1)*7+m)=weight(:,(n-1)*7+m)-alpha*exp(-distant^2/delta^2)*(weight(:,(n-1)*7+m)-train_data_active);  
  66.             end  
  67.         elseif (y>=8)      %结点靠右边  
  68.             for n=y-3:1:10  
  69.                 distant=sqrt((x-m)^2+(y-n)^2);  
  70.                 weight(:,(n-1)*7+m)=weight(:,(n-1)*7+m)-alpha*exp(-distant^2/delta^2)*(weight(:,(n-1)*7+m)-train_data_active);  
  71.             end  
  72.         else  
  73.             for n=y-3:1:y+3  
  74.                 distant=sqrt((x-m)^2+(y-n)^2);  
  75.                 weight(:,(n-1)*7+m)=weight(:,(n-1)*7+m)-alpha*exp(-distant^2/delta^2)*(weight(:,(n-1)*7+m)-train_data_active);  
  76.             end  
  77.         end  
  78.     end  
  79. end  
  80. end  

SOM_neighb2.m

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  1. function [weight]=SOM_neighb2(weight,train_data_active,j_min,delta,alpha)  
  2.   
  3. %% 权值调整幅度分布  
  4. %                          -0.2  
  5. %                           0.2  
  6. %                           0.6  
  7. %        -0.2   0.2   0.6    1    0.6   0.2   -0.2  
  8. %                           0.6  
  9. %                           0.2  
  10. %                          -0.2  
  11. % 单位距离转化比例为0.4  
  12. %% 坐标转换  
  13. [x,y]=line_to_array(j_min);  
  14. % 将1*70向量中的坐标转化为7*10矩阵中的坐标  
  15. %    1   8    ···  
  16. %    7   14   ···  
  17.   
  18. %% 权值调整过程  
  19. %结点靠上边情况  
  20. if (x<=2)  
  21.     for m=1:1:x+2  
  22.         if (y<=2)          %结点靠左边  
  23.             for n=1:1:y+2  
  24.                 distant=sqrt((x-m)^2+(y-n)^2);  
  25.                 weight(:,(n-1)*7+m)=weight(:,(n-1)*7+m)-alpha*exp(-distant^2/delta^2)*(weight(:,(n-1)*7+m)-train_data_active);  
  26.             end  
  27.         elseif (y>=9)      %结点靠右边  
  28.             for n=y-2:1:10  
  29.                 distant=sqrt((x-m)^2+(y-n)^2);  
  30.                 weight(:,(n-1)*7+m)=weight(:,(n-1)*7+m)-alpha*exp(-distant^2/delta^2)*(weight(:,(n-1)*7+m)-train_data_active);  
  31.             end  
  32.         else  
  33.             for n=y-2:1:y+2  
  34.                 distant=sqrt((x-m)^2+(y-n)^2);  
  35.                 weight(:,(n-1)*7+m)=weight(:,(n-1)*7+m)-alpha*exp(-distant^2/delta^2)*(weight(:,(n-1)*7+m)-train_data_active);  
  36.             end  
  37.         end  
  38.     end  
  39.     %结点靠下边情况  
  40. elseif (x>=6)  
  41.     for m=x-2:1:7  
  42.       if (y<=2)          %结点靠左边  
  43.             for n=1:1:y+2  
  44.                 distant=sqrt((x-m)^2+(y-n)^2);  
  45.                 weight(:,(n-1)*7+m)=weight(:,(n-1)*7+m)-alpha*exp(-distant^2/delta^2)*(weight(:,(n-1)*7+m)-train_data_active);  
  46.             end  
  47.         elseif (y>=9)      %结点靠右边  
  48.             for n=y-2:1:10  
  49.                 distant=sqrt((x-m)^2+(y-n)^2);  
  50.                 weight(:,(n-1)*7+m)=weight(:,(n-1)*7+m)-alpha*exp(-distant^2/delta^2)*(weight(:,(n-1)*7+m)-train_data_active);  
  51.             end  
  52.         else  
  53.             for n=y-2:1:y+2  
  54.                 distant=sqrt((x-m)^2+(y-n)^2);  
  55.                 weight(:,(n-1)*7+m)=weight(:,(n-1)*7+m)-alpha*exp(-distant^2/delta^2)*(weight(:,(n-1)*7+m)-train_data_active);  
  56.             end  
  57.       end  
  58.     end  
  59.     %结点正好在中间  
  60. else  
  61.     for m=x-2:1:x+2  
  62.          if (y<=2)          %结点靠左边  
  63.             for n=1:1:y+2  
  64.                 distant=sqrt((x-m)^2+(y-n)^2);  
  65.                 weight(:,(n-1)*7+m)=weight(:,(n-1)*7+m)-alpha*exp(-distant^2/delta^2)*(weight(:,(n-1)*7+m)-train_data_active);  
  66.             end  
  67.         elseif (y>=9)      %结点靠右边  
  68.             for n=y-2:1:10  
  69.                 distant=sqrt((x-m)^2+(y-n)^2);  
  70.                 weight(:,(n-1)*7+m)=weight(:,(n-1)*7+m)-alpha*exp(-distant^2/delta^2)*(weight(:,(n-1)*7+m)-train_data_active);  
  71.             end  
  72.         else  
  73.             for n=y-2:1:y+2  
  74.                 distant=sqrt((x-m)^2+(y-n)^2);  
  75.                 weight(:,(n-1)*7+m)=weight(:,(n-1)*7+m)-alpha*exp(-distant^2/delta^2)*(weight(:,(n-1)*7+m)-train_data_active);  
  76.             end  
  77.         end  
  78.     end  
  79. end  
  80. end  

SOM_neighb1.m

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  1. function [weight]=SOM_neighb1(weight,train_data_active,j_min,delta,alpha)  
  2.   
  3. %% 权值调整幅度分布  
  4. %                          -0.2  
  5. %                           0.2  
  6. %                           0.6  
  7. %        -0.2   0.2   0.6    1    0.6   0.2   -0.2  
  8. %                           0.6  
  9. %                           0.2  
  10. %                          -0.2  
  11. % 单位距离转化比例为0.4  
  12. %% 坐标转换  
  13. [x,y]=line_to_array(j_min);  
  14. % 将1*70向量中的坐标转化为7*10矩阵中的坐标  
  15. %    1   8    ···  
  16. %    7   14   ···  
  17.   
  18. %% 权值调整过程  
  19. %结点靠上边情况  
  20. if (x<=1)  
  21.     for m=1:1:x+1  
  22.         if (y<=1)          %结点靠左边  
  23.             for n=1:1:y+3  
  24.                 distant=sqrt((x-m)^2+(y-n)^2);  
  25.                 weight(:,(n-1)*7+m)=weight(:,(n-1)*7+m)-alpha*exp(-distant^2/delta^2)*(weight(:,(n-1)*7+m)-train_data_active);  
  26.             end  
  27.         elseif (y>=10)      %结点靠右边  
  28.             for n=y-1:1:10  
  29.                 distant=sqrt((x-m)^2+(y-n)^2);  
  30. weight(:,(n-1)*7+m)=weight(:,(n-1)*7+m)-alpha*exp(-distant^2/delta^2)*(weight(:,(n-1)*7+m)-train_data_active);  
  31.             end  
  32.         else  
  33.             for n=y-1:1:y+1  
  34.                 distant=sqrt((x-m)^2+(y-n)^2);  
  35.                 weight(:,(n-1)*7+m)=weight(:,(n-1)*7+m)-alpha*exp(-distant^2/delta^2)*(weight(:,(n-1)*7+m)-train_data_active);  
  36.             end  
  37.         end  
  38.     end  
  39.     %结点靠下边情况  
  40. elseif (x>=7)  
  41.     for m=x-3:1:7  
  42.         if (y<=1)          %结点靠左边  
  43.             for n=1:1:y+3  
  44.                 distant=sqrt((x-m)^2+(y-n)^2);  
  45.                 weight(:,(n-1)*7+m)=weight(:,(n-1)*7+m)-alpha*exp(-distant^2/delta^2)*(weight(:,(n-1)*7+m)-train_data_active);  
  46.             end  
  47.         elseif (y>=10)      %结点靠右边  
  48.             for n=y-1:1:10  
  49.                 distant=sqrt((x-m)^2+(y-n)^2);  
  50. weight(:,(n-1)*7+m)=weight(:,(n-1)*7+m)-alpha*exp(-distant^2/delta^2)*(weight(:,(n-1)*7+m)-train_data_active);  
  51.             end  
  52.         else  
  53.             for n=y-1:1:y+1  
  54.                 distant=sqrt((x-m)^2+(y-n)^2);  
  55.                 weight(:,(n-1)*7+m)=weight(:,(n-1)*7+m)-alpha*exp(-distant^2/delta^2)*(weight(:,(n-1)*7+m)-train_data_active);  
  56.             end  
  57.         end  
  58.     end  
  59.     %结点正好在中间  
  60. else  
  61.     for m=x-1:1:x+1  
  62.         if (y<=1)          %结点靠左边  
  63.             for n=1:1:y+3  
  64.                 distant=sqrt((x-m)^2+(y-n)^2);  
  65.                 weight(:,(n-1)*7+m)=weight(:,(n-1)*7+m)-alpha*exp(-distant^2/delta^2)*(weight(:,(n-1)*7+m)-train_data_active);  
  66.             end  
  67.         elseif (y>=10)      %结点靠右边  
  68.             for n=y-1:1:10  
  69.                 distant=sqrt((x-m)^2+(y-n)^2);  
  70. weight(:,(n-1)*7+m)=weight(:,(n-1)*7+m)-alpha*exp(-distant^2/delta^2)*(weight(:,(n-1)*7+m)-train_data_active);  
  71.             end  
  72.         else  
  73.             for n=y-1:1:y+1  
  74.                 distant=sqrt((x-m)^2+(y-n)^2);  
  75.                 weight(:,(n-1)*7+m)=weight(:,(n-1)*7+m)-alpha*exp(-distant^2/delta^2)*(weight(:,(n-1)*7+m)-train_data_active);  
  76.             end  
  77.         end  
  78.     end  
  79. end  
  80. end  

SOM_neighb0.m

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  1. function [weight]=SOM_neighb0(weight,train_data_active,j_min,alpha)  
  2. weight(:,j_min)=weight(:,j_min)+alpha*(weight(:,j_min)-train_data_active);  
  3. end  

line_to_array.m

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  1. function [x,y]=line_to_array(j_min)  
  2. % 将1*70向量中的坐标转化为7*10矩阵中的坐标  
  3. %    1   8    ···  
  4. %    7   14   ···  
  5. y=ceil(j_min/7);  
  6. x=rem(j_min,7);  
  7. end  


四、结果显示

不同初始条件的结果图

自组织神经网络SOM原理——结合例子MATLAB实现

自组织神经网络SOM原理——结合例子MATLAB实现

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