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：


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》
2，《数值分析Matlab二维正态(高斯)分布以及协方差矩阵》