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Commit 6be54cc4 authored by Tiago Peixoto's avatar Tiago Peixoto
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Add personalization and edge weights to PageRank code

parent 066411ac
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src/graph/centrality/graph_pagerank.cc
View file @ 6be54cc4
......@@ -18,7 +18,7 @@
#include "graph_filtering.hh"
#include <boost/python.hpp>
#include <boost/lambda/bind.hpp>
#include <boost/bind.hpp>
#include "graph.hh"
#include "graph_selectors.hh"
......@@ -28,18 +28,39 @@ using namespace std;
using namespace boost;
using namespace graph_tool;
size_t pagerank(GraphInterface& g, boost::any rank, double d, double epslon,
size_t max_iter)
size_t pagerank(GraphInterface& g, boost::any rank, boost::any pers,
boost::any weight, double d, double epsilon, size_t max_iter)
{
if (!belongs<writable_vertex_scalar_properties>()(rank))
throw ValueException("vertex property must be writable");
if (!belongs<vertex_floating_properties>()(rank))
throw ValueException("rank vertex property must have a floating-point value type");
if (!pers.empty() && !belongs<vertex_scalar_properties>()(pers))
throw ValueException("personalization vertex property must have a scalar value type");
typedef ConstantPropertyMap<double, GraphInterface::vertex_t> pers_map_t;
typedef mpl::push_back<vertex_scalar_properties, pers_map_t>::type
pers_props_t;
if(pers.empty())
pers = pers_map_t(1.0 / g.GetNumberOfVertices());
typedef ConstantPropertyMap<double, GraphInterface::edge_t> weight_map_t;
typedef mpl::push_back<edge_scalar_properties, weight_map_t>::type
weight_props_t;
if (!weight.empty() && !belongs<edge_scalar_properties>()(weight))
throw ValueException("weight edge property must have a scalar value type");
if(weight.empty())
weight = weight_map_t(1.0);
size_t iter;
run_action<>()
(g, bind<void>(get_pagerank(),
_1, g.GetVertexIndex(), _2, d,
epslon, max_iter, ref(iter)),
writable_vertex_scalar_properties())(rank);
_1, g.GetVertexIndex(), _2, _3, _4, d,
epsilon, max_iter, ref(iter)),
vertex_floating_properties(),
pers_props_t(), weight_props_t())(rank, pers, weight);
return iter;
}
......
src/graph/centrality/graph_pagerank.hh
View file @ 6be54cc4
......@@ -29,15 +29,16 @@ using namespace boost;
struct get_pagerank
{
template <class Graph, class VertexIndex, class RankMap>
template <class Graph, class VertexIndex, class RankMap, class PerMap,
class Weight>
void operator()(Graph& g, VertexIndex vertex_index, RankMap rank,
double damping, double epslon, size_t max_iter,
size_t& iter) const
PerMap pers, Weight weight, double damping, double epsilon,
size_t max_iter, size_t& iter) const
{
typedef typename property_traits<RankMap>::value_type rank_type;
size_t NV = HardNumVertices()(g);
RankMap r_temp(vertex_index,num_vertices(g));
RankMap r_temp(vertex_index, num_vertices(g));
RankMap deg(vertex_index, num_vertices(g));
// init ranks
int i, N = num_vertices(g);
......@@ -48,13 +49,18 @@ struct get_pagerank
typename graph_traits<Graph>::vertex_descriptor v = vertex(i, g);
if (v == graph_traits<Graph>::null_vertex())
continue;
rank[v] = 1.0 / NV;
put(rank, v, get(pers, v));
typename graph_traits<Graph>::out_edge_iterator e, e_end;
put(deg, v, 0);
for (tie(e, e_end) = out_edges(v, g); e!= e_end; ++e)
put(deg, v, get(deg, v) + get(weight, *e));
}
rank_type delta = epslon + 1;
rank_type delta = epsilon + 1;
rank_type d = damping;
iter = 0;
while (delta >= epslon)
while (delta >= epsilon)
{
delta = 0;
int i, N = num_vertices(g);
......@@ -74,11 +80,12 @@ struct get_pagerank
{
typename graph_traits<Graph>::vertex_descriptor s =
source(*e, g);
r += get(rank, s) / out_degree(s, g);
r += (get(rank, s) * get(weight, *e)) / get(deg, s);
}
put(r_temp, v, (1.0 - d) / NV + d * r);
delta += abs(get(r_temp, v) - get(rank,v));
put(r_temp, v, (1.0 - d) * get(pers, v) + d * r);
delta += abs(get(r_temp, v) - get(rank, v));
}
swap(r_temp, rank);
++iter;
......
src/graph_tool/centrality/__init__.py
View file @ 6be54cc4
......@@ -51,8 +51,8 @@ __all__ = ["pagerank", "betweenness", "central_point_dominance", "eigentrust",
"trust_transitivity"]
def pagerank(g, damping=0.8, prop=None, epsilon=1e-6, max_iter=None,
ret_iter=False):
def pagerank(g, damping=0.85, pers=None, weight=None, prop=None, epsilon=1e-6,
max_iter=None, ret_iter=False):
r"""
Calculate the PageRank of each vertex.
......@@ -60,8 +60,13 @@ def pagerank(g, damping=0.8, prop=None, epsilon=1e-6, max_iter=None,
----------
g : :class:`~graph_tool.Graph`
Graph to be used.
damping : float, optional (default: 0.8)
damping : float, optional (default: 0.85)
Damping factor.
pers : :class:`~graph_tool.PropertyMap`, optional (default: None)
Personalization vector. If omitted, a constant value of :math:`1/N`
will be used.
weight : :class:`~graph_tool.PropertyMap`, optional (default: None)
Edge weights. If omitted, a constant value of 1 will be used.
prop : :class:`~graph_tool.PropertyMap`, optional (default: None)
Vertex property map to store the PageRank values.
epsilon : float, optional (default: 1e-6)
......@@ -90,13 +95,30 @@ def pagerank(g, damping=0.8, prop=None, epsilon=1e-6, max_iter=None,
.. math::
PR(v) = \frac{1-d}{N} + d \sum_{w \in \Gamma^{-}(v)}
\frac{PR (w)}{d^{+}(w)}
PR(v) = \frac{1-d}{N} + d \sum_{u \in \Gamma^{-}(v)}
\frac{PR (u)}{d^{+}(u)}
where :math:`\Gamma^{-}(v)` are the in-neighbours of v, :math:`d^{+}(w)` is
the out-degree of w, and d is a damping factor.
The implemented algorithm progressively iterates the above condition, until
If a personalization property :math:`p(v)` is given, the definition becomes:
.. math::
PR(v) = (1-d)p(v) + d \sum_{u \in \Gamma^{-}(v)}
\frac{PR (u)}{d^{+}(u)}
If edge weights are also given, the equation is then generalized to:
.. math::
PR(v) = (1-d)p(v) + d \sum_{u \in \Gamma^{-}(v)}
\frac{PR (u) w_{u\to v}}{d^{+}(u)}
where :math:`d^{+}(u)=\sum_{y}A_{u,y}w_{u\to y}` is redefined to be the sum
of the weights of the out-going edges from u.
The implemented algorithm progressively iterates the above equations, until
it no longer changes, according to the parameter epsilon. It has a
topology-dependent running time.
......@@ -104,28 +126,55 @@ def pagerank(g, damping=0.8, prop=None, epsilon=1e-6, max_iter=None,
Examples
--------
>>> from numpy.random import poisson, seed
>>> from numpy.random import random, poisson, seed
>>> seed(42)
>>> g = gt.random_graph(100, lambda: (poisson(3), poisson(3)))
>>> pr = gt.pagerank(g)
>>> print pr.a
[ 0.0087012 0.01734503 0.0047588 0.00453451 0.002 0.01265973
0.0060965 0.00680647 0.00813758 0.00862694 0.00518331 0.00491948
0.00748761 0.00528322 0.00601439 0.00639214 0.013249 0.0068361
0.01026087 0.00909041 0.01102634 0.0056291 0.002 0.00308401
0.00907272 0.0035584 0.00955833 0.00232 0.00410904 0.00887352
0.00474244 0.00661384 0.01263138 0.00745946 0.00841104 0.00949735
0.01059004 0.00944125 0.00264336 0.00861976 0.002 0.00253333
0.00659745 0.00698895 0.01027991 0.00776186 0.00579061 0.01128291
0.00232 0.01183673 0.00389293 0.01724249 0.0047967 0.01093172
0.00459377 0.01094803 0.00802747 0.00447822 0.01046185 0.00253333
0.00822962 0.00402102 0.00727797 0.00750763 0.00417424 0.002
0.00898431 0.00929422 0.00696827 0.00693413 0.01026798 0.002
0.00677507 0.00856227 0.00772329 0.01090938 0.01144107 0.00594142
0.00544564 0.0064372 0.00402752 0.00729768 0.01404475 0.002
0.00318314 0.00373451 0.00256223 0.01058081 0.01024193 0.0082748
0.00496463 0.00729605 0.00486213 0.01421478 0.00656225 0.00316644
0.01553884 0.005844 0.02039237 0.01478031]
[ 0.00782362 0.01642353 0.00420484 0.0038825 0.0015 0.01145378
0.00514203 0.00593481 0.00743705 0.00785063 0.00446447 0.00440222
0.00684158 0.00463226 0.00518308 0.0056288 0.01207045 0.00617264
0.00958574 0.00817165 0.01041552 0.00508079 0.0015 0.00249411
0.00842537 0.00293099 0.00873296 0.001755 0.003371 0.00817938
0.00406813 0.00576584 0.01188752 0.00674565 0.00758134 0.00855306
0.00975204 0.00823918 0.00209855 0.00753858 0.0015 0.001925
0.00593262 0.00603431 0.00977679 0.00707922 0.00529399 0.01048882
0.001755 0.0111949 0.0032813 0.01591077 0.00407595 0.01015827
0.00383036 0.01024311 0.00714593 0.00379142 0.00955729 0.001925
0.00737848 0.00352088 0.00654273 0.00676324 0.00353259 0.0015
0.00809045 0.00864939 0.00626611 0.00632213 0.00939761 0.0015
0.00584767 0.0077272 0.00688094 0.01010526 0.01071083 0.00550524
0.0045327 0.00577072 0.00337711 0.00637928 0.01295484 0.0015
0.00265875 0.003245 0.00203456 0.00969993 0.00908983 0.00759961
0.00428542 0.00674196 0.0043264 0.01339053 0.00570051 0.00253539
0.01464169 0.00505055 0.01919599 0.01413612]
Now with a personalization vector, and edge weights:
>>> w = g.new_edge_property("double")
>>> w.a = random(g.num_edges())
>>> p = g.new_vertex_property("double")
>>> p.a = random(g.num_vertices())
>>> p.a /= p.a.sum()
>>> pr = gt.pagerank(g, pers=p, weight=w)
>>> print pr.a
[ 0.01693559 0.01316915 0.00369907 0.00245658 0.00092715 0.01380721
0.00703909 0.00407121 0.00816254 0.00880131 0.0035886 0.0050914
0.00815843 0.00624021 0.0069828 0.00647311 0.01260669 0.00884083
0.01324534 0.01103024 0.01417902 0.00309344 0.00250025 0.00153889
0.00969556 0.00491575 0.00552323 0.00300698 0.00327355 0.00829017
0.00274335 0.00440865 0.01436394 0.00671045 0.00788395 0.01092875
0.0126331 0.00789263 0.00422443 0.00745144 0.00148972 0.00198663
0.00476339 0.00800871 0.01468149 0.00971962 0.00446663 0.01333257
0.00085768 0.01044298 0.00286075 0.02119469 0.00406517 0.01317145
0.00280023 0.0143227 0.00867722 0.00234863 0.01180399 0.00298827
0.0049022 0.00532752 0.00603759 0.00766617 0.00293739 0.00238803
0.00863735 0.01110095 0.00660816 0.00170262 0.00884469 0.00300867
0.00441168 0.00630793 0.00424727 0.00906709 0.0135949 0.00890726
0.00267835 0.00615783 0.0045653 0.00720592 0.00996495 0.0009367
0.00233309 0.00265909 0.00211686 0.01277934 0.01284484 0.00625721
0.00487027 0.00852522 0.00403389 0.01817233 0.00573321 0.0038696
0.00932334 0.00515806 0.01601592 0.0167547 ]
References
----------
......@@ -133,6 +182,9 @@ def pagerank(g, damping=0.8, prop=None, epsilon=1e-6, max_iter=None,
.. [lawrence-pagerank-1998] P. Lawrence, B. Sergey, M. Rajeev, W. Terry,
"The pagerank citation ranking: Bringing order to the web", Technical
report, Stanford University, 1998
.. [Langville-survey-2005] A. N. Langville, C. D. Meyer, "A Survey of
Eigenvector Methods for Web Information Retrieval", SIAM Review, vol. 47,
no. 1, pp. 135-161, 2005, :DOI:`10.1137/S0036144503424786`
"""
if max_iter == None:
......@@ -140,8 +192,9 @@ def pagerank(g, damping=0.8, prop=None, epsilon=1e-6, max_iter=None,
if prop == None:
prop = g.new_vertex_property("double")
ic = libgraph_tool_centrality.\
get_pagerank(g._Graph__graph, _prop("v", g, prop), damping, epsilon,
max_iter)
get_pagerank(g._Graph__graph, _prop("v", g, prop),
_prop("v", g, pers), _prop("e", g, weight),
damping, epsilon, max_iter)
if ret_iter:
return prop, ic
else:
......
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