Matlab数值分析K-means聚类算法

桃扇骨 2024-02-18 17:13 38阅读 0赞

我写的附录文章1简单介绍了K-means聚类算法。Matlab提供了专用函数kmeans用于聚类的质心。  
假设随机生成两维样本数据，然后用kmeans算出聚类并标记出质心：

r1=randn(5,2)-2
    r2=randn(5,2)+2
    X=[r1;r2];
    
    opts = statset('Display','final');
    [idx,C] = kmeans(X,2,'Replicates',2,'Options',opts);
    
    C%质心
    
    cluster1=[X(idx==1,1),X(idx==1,2)] %簇1
    cluster2=[X(idx==2,1),X(idx==2,2)] %簇2
    
    figure;
    plot(X(idx==1,1),X(idx==1,2),'g^','MarkerSize',5);
    hold on;
    
    plot(X(idx==2,1),X(idx==2,2),'b.','MarkerSize',15);
    hold on;
    
    plot(C(:,1),C(:,2),'r.','MarkerSize',30,'LineWidth',3);
    hold on;
    
    legend('聚类C1','聚类C2','质心','Location','NW');

运行产生的随机试验数据：

r1 =
    
       -1.9197   -1.5771
       -2.8738   -2.0885
       -2.4520   -2.2704
       -1.9906    0.0474
       -3.3071   -0.5084
    
    
    r2 =
    
        1.0730    2.0887
        2.7819    1.6868
        3.1847    1.7797
        2.9300    2.6951
        2.9886    2.4277
    
    Replicate 1, 2 iterations, total sum of distances = 9.16468.
    Replicate 2, 2 iterations, total sum of distances = 9.16468.
    Best total sum of distances = 9.16468
    
    C =
    
        2.5916    2.1356
       -2.5086   -1.2794
    
    
    cluster1 =
    
        1.0730    2.0887
        2.7819    1.6868
        3.1847    1.7797
        2.9300    2.6951
        2.9886    2.4277
    
    
    cluster2 =
    
       -1.9197   -1.5771
       -2.8738   -2.0885
       -2.4520   -2.2704
       -1.9906    0.0474
       -3.3071   -0.5084

r1和r2是随机产生的原始二维坐标点。经过K-means聚类后，根据两个质心，归入到两簇：C1簇和C2簇。

结果如图：  
![20171214204228955][]  
  
附录:  
1,《人工智能AI常见的经典K-means聚类算法原理和工作过程》链接：http://blog.csdn.net/zhangphil/article/details/78783629  
2，《数值分析Matlab二维正态(高斯)分布以及协方差矩阵》链接：http://blog.csdn.net/zhangphil/article/details/78803538

[20171214204228955]: https://image.dandelioncloud.cn/pgy_files/images/2024/01/29/be836e44a74c4b8eb105c1ba48816a03.png