完整的最简单的谱聚类python代码

http://blog.csdn.net/waleking/article/details/7584084

针对karate_club数据集，做了谱聚类。由于是2-way clustering，比较简单，得到了图的新的表示空间之后，没有做k-means，仅仅针对正规化后的拉普拉斯矩阵的第二特征值做了符号判断，这和 Spectral Clustering Tutorial 一文中的描述一致。

引用了numpy scipy matplotlib networkx包

#coding=utf-8

#MSC means Multiple Spectral Clustering 

import numpy as np

import scipy as sp

import scipy.linalg as linalg

import networkx as nx

import matplotlib.pyplot as plt

def getNormLaplacian(W):

 """input matrix W=(w_ij)

 "compute D=diag(d1,...dn)

 "and L=D-W

 "and Lbar=D^(-1/2)LD^(-1/2)

 "return Lbar

 """

 d=[np.sum(row) for row in W]

 D=np.diag(d)

 L=D-W

 #Dn=D^(-1/2)

 Dn=np.power(np.linalg.matrix_power(D,-1),0.5)

 Lbar=np.dot(np.dot(Dn,L),Dn)

 return Lbar

def getKSmallestEigVec(Lbar,k):

 """input

 "matrix Lbar and k

 "return

 "k smallest eigen values and their corresponding eigen vectors

 """

 eigval,eigvec=linalg.eig(Lbar)

 dim=len(eigval)

 #查找前k小的eigval

 dictEigval=dict(zip(eigval,range(0,dim)))

 kEig=np.sort(eigval)[0:k]

 ix=[dictEigval[k] for k in kEig]

 return eigval[ix],eigvec[:,ix]

def checkResult(Lbar,eigvec,eigval,k):

 """

 "input

 "matrix Lbar and k eig values and k eig vectors

 "print norm(Lbar*eigvec[:,i]-lamda[i]*eigvec[:,i])

 """

 check=[np.dot(Lbar,eigvec[:,i])-eigval[i]*eigvec[:,i] for i in range(0,k)]

 length=[np.linalg.norm(e) for e in check]/np.spacing(1)

 print("Lbar*v-lamda*v are %s*%s" % (length,np.spacing(1)))

g=nx.karate_club_graph()

nodeNum=len(g.nodes())

m=nx.to_numpy_matrix(g)

Lbar=getNormLaplacian(m)

k=2

kEigVal,kEigVec=getKSmallestEigVec(Lbar,k)

print("k eig val are %s" % kEigVal)

print("k eig vec are %s" % kEigVec)

checkResult(Lbar,kEigVec,kEigVal,k)

#跳过k means，用最简单的符号判别的方法来求点的归属

clusterA=[i for i in range(0,nodeNum) if kEigVec[i,1]>0]

clusterB=[i for i in range(0,nodeNum) if kEigVec[i,1]<0]

#draw graph

colList=dict.fromkeys(g.nodes())

for node,score in colList.items():

 if node in clusterA:

  colList[node]=0

 else:

  colList[node]=0.6

plt.figure(figsize=(8,8))

pos=nx.spring_layout(g)

nx.draw_networkx_edges(g,pos,alpha=0.4)

nx.draw_networkx_nodes(g,pos,nodelist=colList.keys(),

  node_color=colList.values(),

  cmap=plt.cm.Reds_r)

nx.draw_networkx_labels(g,pos,font_size=10,font_family='sans-serif')

plt.axis('off')

plt.title("karate_club spectral clustering")

plt.savefig("spectral_clustering_result.png")

plt.show()