K-means的源码实现
一般情况下，我们通过C++/Matlab/Python等语言进行实现K-means算法，结合近期我刚刚学的C++，先从C++实现谈起，C++里面我们一般采用的是OpenCV库中写好的K-means函数，即cvKmeans2，首先来看函数原型：
从OpenCV manual看到的是：
int cvKMeans2(const CvArr* samples, int nclusters,
CvArr* labels, CvTermCriteria termcrit,
int attempts=1, CvRNG* rng=0,int flags=0,
CvArr* centers=0,double* compactness=0);
由于除去已经确定的参数，我们自己需要输入的为：
void cvKMeans2(
const CvArr* samples, //输入样本的浮点矩阵，每个样本一行。
int cluster_count, //所给定的聚类数目
* labels, //输出整数向量：每个样本对应的类别标识
CvTermCriteria termcrit //指定聚类的最大迭代次数和／或精度（两次迭代引起的聚类中心的移动距离）
);
其使用例程为：
1 #ifdef _CH_
2 #pragma package <opencv>
3 #endif
4
5 #define CV_NO_BACKWARD_COMPATIBILITY
6
7 #ifndef _EiC
8 #include "cv.h"
9 #include "highgui.h"
10 #include <stdio.h>
11 #endif
12
13 int main( int argc, char** argv )
14 {
15 #define MAX_CLUSTERS 5 //设置类别的颜色，个数（《=5）
16 CvScalar color_tab[MAX_CLUSTERS];
17 IplImage* img = cvCreateImage( cvSize( 500, 500 ), 8, 3 );
18 CvRNG rng = cvRNG(-1);
19 CvPoint ipt;
20
21 color_tab[0] = CV_RGB(255,0,0);
22 color_tab[1] = CV_RGB(0,255,0);
23 color_tab[2] = CV_RGB(100,100,255);
24 color_tab[3] = CV_RGB(255,0,255);
25 color_tab[4] = CV_RGB(255,255,0);
26
27 cvNamedWindow( "clusters", 1 );
28
29 for(;;)
30 {
31 char key;
32 int k, cluster_count = cvRandInt(&rng)%MAX_CLUSTERS + 1;
33 int i, sample_count = cvRandInt(&rng)%1000 + 1;
34 CvMat* points = cvCreateMat( sample_count, 1, CV_32FC2 );
35 CvMat* clusters = cvCreateMat( sample_count, 1, CV_32SC1 );
36 cluster_count = MIN(cluster_count, sample_count);
37
38 /** generate random sample from multigaussian distribution */
39 for( k = 0; k < cluster_count; k++ )
40 {
41 CvPoint center;
42 CvMat point_chunk;
43 center.x = cvRandInt(&rng)%img->width;
44 center.y = cvRandInt(&rng)%img->height;
45 cvGetRows( points, &point_chunk, k*sample_count/cluster_count,
46 k == cluster_count - 1 ? sample_count :
47 (k+1)*sample_count/cluster_count, 1 );
48
49 cvRandArr( &rng, &point_chunk, CV_RAND_NORMAL,
50 cvScalar(center.x,center.y,0,0),
51 cvScalar(img->width*0.1,img->height*0.1,0,0));
52 }
53
54 /** shuffle samples */
55 for( i = 0; i < sample_count/2; i++ )
56 {
57 CvPoint2D32f* pt1 = (CvPoint2D32f*)points->data.fl + cvRandInt(&rng)%sample_count;
58 CvPoint2D32f* pt2 = (CvPoint2D32f*)points->data.fl + cvRandInt(&rng)%sample_count;
59 CvPoint2D32f temp;
60 CV_SWAP( *pt1, *pt2, temp );
61 }
62
63 printf( "iterations=%d\n", cvKMeans2( points, cluster_count, clusters,
64 cvTermCriteria( CV_TERMCRIT_EPS+CV_TERMCRIT_ITER, 10, 1.0 ),
65 5, 0, 0, 0, 0 ));
66
67 cvZero( img );
68
69 for( i = 0; i < sample_count; i++ )
70 {
71 int cluster_idx = clusters->data.i[i];
72 ipt.x = (int)points->data.fl[i*2];
73 ipt.y = (int)points->data.fl[i*2+1];
74 cvCircle( img, ipt, 2, color_tab[cluster_idx], CV_FILLED, CV_AA, 0 );
75 }
76
77 cvReleaseMat( &points );
78 cvReleaseMat( &clusters );
79
80 cvShowImage( "clusters", img );
81
82 key = (char) cvWaitKey(0);
83 if( key == 27 || key == 'q' || key == 'Q' ) // 'ESC'
84 break;
85 }
86
87 cvDestroyWindow( "clusters" );
88 return 0;
89 }
90
91 #ifdef _EiC
92 main(1,"kmeans.c");
93 #endif
至于cvKmeans2函数的具体实现细节，可参见OpenCV源码
下面是Python的实现代码（网上所找）：
1 #!/usr/bin/python
2
3 from __future__ import with_statement
4 import cPickle as pickle
5 from matplotlib import pyplot
6 from numpy import zeros, array, tile
7 from scipy.linalg import norm
8 import numpy.matlib as ml
9 import random
10
11 def kmeans(X, k, observer=None, threshold=1e-15, maxiter=300):
12 N = len(X)
13 labels = zeros(N, dtype=int)
14 centers = array(random.sample(X, k))
15 iter = 0
16
17 def calc_J():
18 sum = 0
19 for i in xrange(N):
20 sum += norm(X[i]-centers[labels[i]])
21 return sum
22
23 def distmat(X, Y):
24 n = len(X)
25 m = len(Y)
26 xx = ml.sum(X*X, axis=1)
27 yy = ml.sum(Y*Y, axis=1)
28 xy = ml.dot(X, Y.T)
29
30 return tile(xx, (m, 1)).T+tile(yy, (n, 1)) - 2*xy
31
32 Jprev = calc_J()
33 while True:
34 # notify the observer
35 if observer is not None:
36 observer(iter, labels, centers)
37
38 # calculate distance from x to each center
39 # distance_matrix is only available in scipy newer than 0.7
40 # dist = distance_matrix(X, centers)
41 dist = distmat(X, centers)
42 # assign x to nearst center
43 labels = dist.argmin(axis=1)
44 # re-calculate each center
45 for j in range(k):
46 idx_j = (labels == j).nonzero()
47 centers[j] = X[idx_j].mean(axis=0)
48
49 J = calc_J()
50 iter += 1
51
52 if Jprev-J < threshold:
53 break
54 Jprev = J
55 if iter >= maxiter:
56 break
57
58 # final notification
59 if observer is not None:
60 observer(iter, labels, centers)
61
62 if __name__ == '__main__':
63 # load previously generated points
64 with open('cluster.pkl') as inf:
65 samples = pickle.load(inf)
66 N = 0
67 for smp in samples:
68 N += len(smp[0])
69 X = zeros((N, 2))
70 idxfrm = 0
71 for i in range(len(samples)):
72 idxto = idxfrm + len(samples[i][0])
73 X[idxfrm:idxto, 0] = samples[i][0]
74 X[idxfrm:idxto, 1] = samples[i][1]
75 idxfrm = idxto
76
77 def observer(iter, labels, centers):
78 print "iter %d." % iter
79 colors = array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
80 pyplot.plot(hold=False) # clear previous plot
81 pyplot.hold(True)
82
83 # draw points
84 data_colors=[colors[lbl] for lbl in labels]
85 pyplot.scatter(X[:, 0], X[:, 1], c=data_colors, alpha=0.5)
86 # draw centers
87 pyplot.scatter(centers[:, 0], centers[:, 1], s=200, c=colors)
88
89 pyplot.savefig('kmeans/iter_%02d.png' % iter, format='png')
90
91 kmeans(X, 3, observer=observer)
matlab的kmeans实现代码可直接参照其kmeans(X,k)函数的实现源码。