Turn: Complete simplest spectral clustering Python code

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

Spectral clustering is done for Karate_club datasets. Because it is 2-way clustering, relatively simple, got the new representation space of the diagram, did not do K-means, only for the normalized Laplace matrix of the second eigenvalue to do a symbolic judgment, which and spectral clustering Tutorial The description in the article is consistent.

Reference to NumPy scipy matplotlib NETWORKX Package

2. #coding =utf-8
4. #MSC means multiple spectral clustering
6. import NumPy as NP
8. import scipy as sp
10. import scipy.linalg as linalg
12. import Networkx as NX
14. import Matplotlib.pyplot as plt
18. def Getnormlaplacian(W):
20. "" " Input matrix w= (W_IJ)
22. "Compute d=diag (D1,... DN)
24. "and L=d-w
26. "and lbar=d^ ( -1/2) ld^ ( -1/2)
28. "Return Lbar
30. """
32. D=[np.sum (Row) for row in W]
34. D=np.diag (d)
36. L=d-w
38. #Dn =d^ ( -1/2)
40. Dn=np.power (Np.linalg.matrix_power (D,-1),0.5)
42. Lbar=np.dot (Np.dot (dn,l), Dn)
44. return Lbar
48. def Getksmallesteigvec(lbar,k):
50. "" "input
52. "Matrix Lbar and K
54. "Return
56. "K smallest eigen values and their corresponding eigen vectors
58. """
60. Eigval,eigvec=linalg.eig (Lbar)
62. Dim=len (Eigval)
66. #查找前k小的eigval
68. Dicteigval=dict (Zip (Eigval,range (0,dim)))
70. Keig=np.sort (eigval) [0:k]
72. Ix=[dicteigval[k] for K in Keig]
74. return Eigval[ix],eigvec[:,ix]
78. def checkresult(lbar,eigvec,eigval,k):
80. """
82. the input
84. "Matrix Lbar and K Eig values and K Eig vectors
86. "Print norm (Lbar*eigvec[:,i]-lamda[i]*eigvec[:,i])
88. """
90. Check=[np.dot (Lbar,eigvec[:,i])-eigval[i]*eigvec[:,i] for i in range (0,k)]
92. Length=[np.linalg.norm (e) for E in check]/np.spacing (1)
94. Print ("lbar*v-lamda*v is%s*%s"% (length,np.spacing (1)))
98. G=nx.karate_club_graph ()
100. Nodenum=len (G.nodes ())
102. M=nx.to_numpy_matrix (g)
104. Lbar=getnormlaplacian (M)
106. k=2
108. Keigval,keigvec=getksmallesteigvec (Lbar,k)
110. Print ("K Eig Val is%s"% keigval)
112. Print ("K Eig Vec is%s"% Keigvec)
114. Checkresult (Lbar,keigvec,keigval,k)
118. #跳过k means, using the simplest symbolic discriminant method to find the point of attribution
122. Clustera=[i for I in range (0,nodenum) if keigvec[i,1]>0]
124. Clusterb=[i for I in range (0,nodenum) if keigvec[i,1]<0]
128. #draw Graph
130. Collist=dict.fromkeys (G.nodes ())
132. For Node,score in collist.items ():
134. if node in clustera:
136. collist[node]=0
138. Else:
140. collist[node]=0.6
142. Plt.figure (figsize= (8,8))
144. Pos=nx.spring_layout (g)
146. Nx.draw_networkx_edges (g,pos,alpha=0.4)
148. Nx.draw_networkx_nodes (G,pos,nodelist=collist.keys (),
150. Node_color=collist.values (),
152. Cmap=plt.cm.reds_r)
154. Nx.draw_networkx_labels (g,pos,font_size=10,font_family=' Sans-serif ')
156. Plt.axis (' off ')
158. Plt.title ("Karate_club spectral Clustering")
160. Plt.savefig ("Spectral_clustering_result.png")
162. Plt.show ()

Resulting cluster results:

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Turn: Complete simplest spectral clustering Python code