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Last active September 10, 2015 01:37
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python implementation of pagerank
import numpy as np
from scipy.sparse import csc_matrix
def pageRank(G, s = .85, maxerr = .001):
"""
Computes the pagerank for each of the n states.
Used in webpage ranking and text summarization using unweighted
or weighted transitions respectively.
Args
----------
G: matrix representing state transitions
Gij can be a boolean or non negative real number representing the
transition weight from state i to j.
Kwargs
----------
s: probability of following a transition. 1-s probability of teleporting
to another state. Defaults to 0.85
maxerr: if the sum of pageranks between iterations is bellow this we will
have converged. Defaults to 0.001
"""
n = G.shape[0]
# transform G into markov matrix M
M = csc_matrix(G,dtype=np.float)
rsums = np.array(M.sum(1))[:,0]
ri, ci = M.nonzero()
M.data /= rsums[ri]
# bool array of sink states
sink = rsums==0
# Compute pagerank r until we converge
ro, r = np.zeros(n), np.ones(n)
while np.sum(np.abs(r-ro)) > maxerr:
ro = r.copy()
# calculate each pagerank at a time
for i in xrange(0,n):
# inlinks of state i
Ii = np.array(M[:,i].todense())[:,0]
# account for sink states
Si = sink / float(n)
# account for teleportation to state i
Ti = np.ones(n) / float(n)
r[i] = ro.dot( Ii*s + Si*s + Ti*(1-s) )
# return normalized pagerank
return r/sum(r)
if __name__=='__main__':
# Example extracted from 'Introduction to Information Retrieval'
G = np.array([[0,0,1,0,0,0,0],
[0,1,1,0,0,0,0],
[1,0,1,1,0,0,0],
[0,0,0,1,1,0,0],
[0,0,0,0,0,0,1],
[0,0,0,0,0,1,1],
[0,0,0,1,1,0,1]])
print pageRank(G,s=.86)
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