Python实现的Kmeans++算法实例

class =
     2
     2
     2
     1
     1
     1
     1

C =
    4.0629    4.0845
   -0.1341    0.1201

sumd =
    1.2017
    0.2939

D =
   34.3727    0.0184
   29.5644    0.1858
   36.3511    0.0898
    0.1247   37.4801
    0.7537   24.0659
    0.1979   36.7666
    0.1256   36.2149

try:
    import psyco
    psyco.full()
except ImportError:
    pass

FLOAT_MAX = 1e100

class Point:
    __slots__ = ["x", "y", "group"]
    def __init__(self, x=0.0, y=0.0, group=0):
        self.x, self.y, self.group = x, y, group

def generate_points(npoints, radius):
    points = [Point() for _ in xrange(npoints)]

    # note: this is not a uniform 2-d distribution
    for p in points:
        r = random() * radius
        ang = random() * 2 * pi
        p.x = r * cos(ang)
        p.y = r * sin(ang)

    return points

def nearest_cluster_center(point, cluster_centers):
    """Distance and index of the closest cluster center"""
    def sqr_distance_2D(a, b):
        return (a.x - b.x) ** 2  +  (a.y - b.y) ** 2

    min_index = point.group
    min_dist = FLOAT_MAX

    for i, cc in enumerate(cluster_centers):
        d = sqr_distance_2D(cc, point)
        if min_dist > d:
            min_dist = d
            min_index = i

    return (min_index, min_dist)

'''
points是数据点，nclusters是给定的簇类数目
cluster_centers包含初始化的nclusters个中心点，开始都是对象->(0,0,0)
'''

def kpp(points, cluster_centers):
    cluster_centers[0] = copy(choice(points)) #随机选取第一个中心点
    d = [0.0 for _ in xrange(len(points))]  #列表，长度为len(points)，保存每个点离最近的中心点的距离

    for i in xrange(1, len(cluster_centers)):  # i=1...len(c_c)-1
        sum = 0
        for j, p in enumerate(points):
            d[j] = nearest_cluster_center(p, cluster_centers[:i])[1] #第j个数据点p与各个中心点距离的最小值
            sum += d[j]

        sum *= random()

        for j, di in enumerate(d):
            sum -= di
            if sum > 0:
                continue
            cluster_centers[i] = copy(points[j])
            break

    for p in points:
        p.group = nearest_cluster_center(p, cluster_centers)[0]

'''
points是数据点，nclusters是给定的簇类数目
'''
def lloyd(points, nclusters):
    cluster_centers = [Point() for _ in xrange(nclusters)]  #根据指定的中心点个数，初始化中心点，均为(0,0,0)

    # call k++ init
    kpp(points, cluster_centers)   #选择初始种子点

    # 下面是kmeans
    lenpts10 = len(points) >> 10

    changed = 0
    while True:
        # group element for centroids are used as counters
        for cc in cluster_centers:
            cc.x = 0
            cc.y = 0
            cc.group = 0

        for p in points:
            cluster_centers[p.group].group += 1  #与该种子点在同一簇的数据点的个数
            cluster_centers[p.group].x += p.x
            cluster_centers[p.group].y += p.y

        for cc in cluster_centers:    #生成新的中心点
            cc.x /= cc.group
            cc.y /= cc.group

        # find closest centroid of each PointPtr
        changed = 0  #记录所属簇发生变化的数据点的个数
        for p in points:
            min_i = nearest_cluster_center(p, cluster_centers)[0]
            if min_i != p.group:
                changed += 1
                p.group = min_i

        # stop when 99.9% of points are good
        if changed <= lenpts10:
            break

    for i, cc in enumerate(cluster_centers):
        cc.group = i

    return cluster_centers

def print_eps(points, cluster_centers, W=400, H=400):
    Color = namedtuple("Color", "r g b");

    colors = []
    for i in xrange(len(cluster_centers)):
        colors.append(Color((3 * (i + 1) % 11) / 11.0,
                            (7 * i % 11) / 11.0,
                            (9 * i % 11) / 11.0))

    max_x = max_y = -FLOAT_MAX
    min_x = min_y = FLOAT_MAX

    for p in points:
        if max_x < p.x: max_x = p.x
        if min_x > p.x: min_x = p.x
        if max_y < p.y: max_y = p.y
        if min_y > p.y: min_y = p.y

    scale = min(W / (max_x - min_x),
                H / (max_y - min_y))
    cx = (max_x + min_x) / 2
    cy = (max_y + min_y) / 2

    print "%%!PS-Adobe-3.0\n%%%%BoundingBox: -5 -5 %d %d" % (W + 10, H + 10)

    print ("/l {rlineto} def /m {rmoveto} def\n" +
           "/c { .25 sub exch .25 sub exch .5 0 360 arc fill } def\n" +
           "/s { moveto -2 0 m 2 2 l 2 -2 l -2 -2 l closepath " +
           "   gsave 1 setgray fill grestore gsave 3 setlinewidth" +
           " 1 setgray stroke grestore 0 setgray stroke }def")

    for i, cc in enumerate(cluster_centers):
        print ("%g %g %g setrgbcolor" %
               (colors[i].r, colors[i].g, colors[i].b))

        for p in points:
            if p.group != i:
                continue
            print ("%.3f %.3f c" % ((p.x - cx) * scale + W / 2,
                                    (p.y - cy) * scale + H / 2))

        print ("\n0 setgray %g %g s" % ((cc.x - cx) * scale + W / 2,
                                        (cc.y - cy) * scale + H / 2))

    print "\n%%%%EOF"

def main():
    npoints = 30000
    k = 7 # # clusters

    points = generate_points(npoints, 10)
    cluster_centers = lloyd(points, k)
    print_eps(points, cluster_centers)

main()

%   Version: 2013-02-08
%   Authors: Laurent Sorber (Laurent.Sorber@cs.kuleuven.be)

L = [];
L1 = 0;

while length(unique(L)) ~= k

    % The k-means++ initialization.
    C = X(:,1+round(rand*(size(X,2)-1))); %size(X,2)是数据集合X的数据点的数目，C是中心点的集合
    L = ones(1,size(X,2));
    for i = 2:k
        D = X-C(:,L); %-1
        D = cumsum(sqrt(dot(D,D,1))); %将每个数据点与中心点的距离，依次累加
        if D(end) == 0, C(:,i:k) = X(:,ones(1,k-i+1)); return; end
        C(:,i) = X(:,find(rand < D/D(end),1)); %find的第二个参数表示返回的索引的数目
        [~,L] = max(bsxfun(@minus,2*real(C'*X),dot(C,C,1).')); %碉堡了，这句，将每个数据点进行分类。
    end

    % The k-means algorithm.
    while any(L ~= L1)
        L1 = L;
        for i = 1:k, l = L==i; C(:,i) = sum(X(:,l),2)/sum(l); end
        [~,L] = max(bsxfun(@minus,2*real(C'*X),dot(C,C,1).'),[],1);
    end

end

>> [L, C] = kmeanspp(x',2)
L =
     2     2     2     1     1     1     1
C =
    4.4839    0.3699
    3.9913    0.1175