谱聚类--SpectralClustering

谱聚类通常会先对两两样本间求相似度。 然后依据相似度矩阵求出拉普拉斯矩阵，然后将每一个样本映射到拉普拉斯矩阵特诊向量中，最后使用k-means聚类。

scikit-learn开源包中已经有现成的接口能够使用，详细见

http://scikit-learn.org/dev/modules/generated/sklearn.cluster.SpectralClustering.html#sklearn.cluster.SpectralClustering

写了一个測试样例

构造二维空间样本点。 

#!/usr/bin/env python
import random
import numpy as np
import math

index = 0
pointlist = []
fd = open("points.txt", 'w')

for x in np.arange(0.1, 10., 0.5) :
    for y in np.arange(0., 10., 0.1) :
        print >> fd, str(index)+'	'+str(x)+'	'+str(y)
        pointlist.append((index, (x, y)))
        index += 1

for x in np.arange(-10.0, -0.1, 0.5) :
    for y in np.arange(0., 10., 0.1) :
        print >> fd, str(index)+'	'+str(x)+'	'+str(y)
        pointlist.append((index, (x, y)))
        index += 1

for x in np.arange(-10.0, -0.1, 0.5) :
    for y in np.arange(-10.0, 0., 0.1) :
        print >> fd, str(index)+'	'+str(x)+'	'+str(y)
        pointlist.append((index, (x, y)))
        index += 1
fd.close()

def get_dist(pnt1, pnt2) :
    return math.sqrt((pnt1[1][0] - pnt2[1][0])**2 + (pnt1[1][1] - pnt2[1][1])**2)

simfd = open("sim_pnts.txt", 'w')
for pnt1 in pointlist :
    for pnt2 in pointlist :
        index1, index2 = pnt1[0], pnt2[0]
        dist = get_dist(pnt1, pnt2)
        if dist <=0.00001 : 
            print >> simfd, str(index1) + "	"+str(index2) + "	" + "10"
            continue
        sim = 1.0 / dist
        print >> simfd, str(index1) + "	"+str(index2) + "	" + str(sim)
simfd.close()

使用谱聚类：

#!/usr/bin/env python
# Authors:  Emmanuelle Gouillart <emmanuelle.gouillart@normalesup.org>
#           Gael Varoquaux <gael.varoquaux@normalesup.org>
# License: BSD 3 clause

import sys
import numpy as np

from sklearn.cluster import spectral_clustering
from scipy.sparse import coo_matrix

###############################################################################

fid2fname = {}
for line in open("points.txt") :
    line = line.strip().split('	')
    fid2fname.setdefault(int(line[0]), (float(line[1]), float(line[2])))

N = len(fid2fname)
rowlist = []
collist = []
datalist = []
for line in open("sim_pnts.txt") :
    line = line.strip().split('	')
    if len(line) < 3 : continue
    f1, f2, sim = line[:3]
    rowlist.append(int(f1))
    collist.append(int(f2))
    datalist.append(float(sim))

for id in fid2fname :
    rowlist.append(int(id))
    collist.append(int(id))
    datalist.append(1.0)

row = np.array(rowlist)
col = np.array(collist)
data = np.array(datalist)
graph = coo_matrix((data, (row, col)), shape=(N, N))

###############################################################################

# Force the solver to be arpack, since amg is numerically
# unstable on this example
labels = spectral_clustering(graph, n_clusters=3, eigen_solver='arpack')

#print labels
cluster2fid = {}
for index, lab in enumerate(labels) :
    cluster2fid.setdefault(lab, [])
    cluster2fid[lab].append(index)

for index, lab in enumerate(cluster2fid) :
    fd = open("cluster_%s" % index, "w")
    for fid in cluster2fid[lab] :
        print >> fd , fid2fname[fid]

将聚类后的样本可视化：

#!/usr/bin/env python
import matplotlib.pyplot as plt

plt.figure(figsize=(12,6))

cluster_list = []

cluster_0_x = []
cluster_0_y = []
for line in open("cluster_0"):
    line = line.strip().split(',')
    x = float(line[0][1:].strip())
    y = float(line[1][:-1].strip())
    cluster_0_x.append(x)
    cluster_0_y.append(y)

plt.plot(cluster_0_x, cluster_0_y, 'or')


cluster_1_x = []
cluster_1_y = []
for line in open("cluster_1"):
    line = line.strip().split(',')
    x = float(line[0][1:].strip())
    y = float(line[1][:-1].strip())
    cluster_1_x.append(x)
    cluster_1_y.append(y)

plt.plot(cluster_1_x, cluster_1_y, 'xb')

cluster_2_x = []
cluster_2_y = []
for line in open("cluster_2"):
    line = line.strip().split(',')
    x = float(line[0][1:].strip())
    y = float(line[1][:-1].strip())
    cluster_2_x.append(x)
    cluster_2_y.append(y)

plt.plot(cluster_2_x, cluster_2_y, '+g')

plt.show()

不同颜色代表不同的聚类， 能够看到聚类效果还是不错的。