laywerrobot/lib/python3.6/site-packages/gensim/summarization/pagerank_weighted.py
2020-08-27 21:55:39 +02:00

175 lines
4.6 KiB
Python

#!/usr/bin/env python
# -*- coding: utf-8 -*-
#
# Licensed under the GNU LGPL v2.1 - http://www.gnu.org/licenses/lgpl.html
"""This module calculate PageRank [1]_ based on wordgraph.
.. [1] https://en.wikipedia.org/wiki/PageRank
Examples
--------
Calculate Pagerank for words
>>> from gensim.summarization.keywords import get_graph
>>> from gensim.summarization.pagerank_weighted import pagerank_weighted
>>> graph = get_graph("The road to hell is paved with good intentions.")
>>> # result will looks like {'good': 0.70432858653171504, 'hell': 0.051128871128006126, ...}
>>> result = pagerank_weighted(graph)
Build matrix from graph
>>> from gensim.summarization.pagerank_weighted import build_adjacency_matrix
>>> build_adjacency_matrix(graph).todense()
matrix([[ 0., 0., 0., 0., 0.],
[ 0., 0., 1., 0., 0.],
[ 0., 1., 0., 0., 0.],
[ 0., 0., 0., 0., 0.],
[ 0., 0., 0., 0., 0.]])
"""
import numpy
from numpy import empty as empty_matrix
from scipy.linalg import eig
from scipy.sparse import csr_matrix
from scipy.sparse.linalg import eigs
from six.moves import xrange
def pagerank_weighted(graph, damping=0.85):
"""Get dictionary of `graph` nodes and its ranks.
Parameters
----------
graph : :class:`~gensim.summarization.graph.Graph`
Given graph.
damping : float
Damping parameter, optional
Returns
-------
dict
Nodes of `graph` as keys, its ranks as values.
"""
adjacency_matrix = build_adjacency_matrix(graph)
probability_matrix = build_probability_matrix(graph)
pagerank_matrix = damping * adjacency_matrix.todense() + (1 - damping) * probability_matrix
vec = principal_eigenvector(pagerank_matrix.T)
# Because pagerank_matrix is positive, vec is always real (i.e. not complex)
return process_results(graph, vec.real)
def build_adjacency_matrix(graph):
"""Get matrix representation of given `graph`.
Parameters
----------
graph : :class:`~gensim.summarization.graph.Graph`
Given graph.
Returns
-------
:class:`scipy.sparse.csr_matrix`, shape = [n, n]
Adjacency matrix of given `graph`, n is number of nodes.
"""
row = []
col = []
data = []
nodes = graph.nodes()
length = len(nodes)
for i in xrange(length):
current_node = nodes[i]
neighbors_sum = sum(graph.edge_weight((current_node, neighbor)) for neighbor in graph.neighbors(current_node))
for j in xrange(length):
edge_weight = float(graph.edge_weight((current_node, nodes[j])))
if i != j and edge_weight != 0.0:
row.append(i)
col.append(j)
data.append(edge_weight / neighbors_sum)
return csr_matrix((data, (row, col)), shape=(length, length))
def build_probability_matrix(graph):
"""Get square matrix of shape (n, n), where n is number of nodes of the
given `graph`.
Parameters
----------
graph : :class:`~gensim.summarization.graph.Graph`
Given graph.
Returns
-------
numpy.ndarray, shape = [n, n]
Eigenvector of matrix `a`, n is number of nodes of `graph`.
"""
dimension = len(graph.nodes())
matrix = empty_matrix((dimension, dimension))
probability = 1.0 / float(dimension)
matrix.fill(probability)
return matrix
def principal_eigenvector(a):
"""Get eigenvector of square matrix `a`.
Parameters
----------
a : numpy.ndarray, shape = [n, n]
Given matrix.
Returns
-------
numpy.ndarray, shape = [n, ]
Eigenvector of matrix `a`.
"""
# Note that we prefer to use `eigs` even for dense matrix
# because we need only one eigenvector. See #441, #438 for discussion.
# But it doesn't work for dim A < 3, so we just handle this special case
if len(a) < 3:
vals, vecs = eig(a)
ind = numpy.abs(vals).argmax()
return vecs[:, ind]
else:
vals, vecs = eigs(a, k=1)
return vecs[:, 0]
def process_results(graph, vec):
"""Get `graph` nodes and corresponding absolute values of provided eigenvector.
This function is helper for :func:`~gensim.summarization.pagerank_weighted.pagerank_weighted`
Parameters
----------
graph : :class:`~gensim.summarization.graph.Graph`
Given graph.
vec : numpy.ndarray, shape = [n, ]
Given eigenvector, n is number of nodes of `graph`.
Returns
-------
dict
Graph nodes as keys, corresponding elements of eigenvector as values.
"""
scores = {}
for i, node in enumerate(graph.nodes()):
scores[node] = abs(vec[i])
return scores