針對karate_club資料集，做了譜聚類。由於是2-way clustering，比較簡單，得到了圖的新的表示空間之後，沒有做k-means，僅僅針對正規化後的拉普拉斯矩陣的第二特徵值做了符號判斷，這和 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)  #查詢前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) #跳過k means，用最簡單的符號判別的方法來求點的歸屬 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()