Graph::Similarity - Calculate similarity of the vertices in graph(s)
This document describes Graph::Similarity version 0.0.5
use Graph; use Graph::Similarity; my $g = Graph->new; # Use Graph module $g->add_vertices("a","b","c","d","e"); $g->add_edges(['a', 'b'], ['b', 'c'], ['a', 'd'], ['d', 'e']); # Calculate by SimRank my $s = new Graph::Similarity(graph => [$g]); my $method = $s->use('SimRank'); $method->setConstnact(0.8); $method->calculate(); $method->showAllSimilarities; $method->getSimilarity("c","e"); #=============================================== # Or by Coupled Node Edge Scoring my $g1 = Graph->new; $g1->add_vertices("A","B","C"); $g1->add_edges(['A', 'B'], ['B','C']); my $g2 = Graph->new; $g2->add_vertices("a","b","c","d","e"); $g2->add_edges(['a', 'b'], ['b', 'c'], ['a', 'd'], ['d', 'e']); my $method = $s->use('CoupledNodeEdgeScoring'); $method->calculate(); $method->showAllSimilarities; #=============================================== # Or by Similarity Flooding my $g1 = Graph->new(multiedged => 1); $g1->add_vertices("I","coffee","apple","swim"); $g1->add_edge_by_id("I", "coffee", "drink"); $g1->add_edge_by_id("I", "swim", "can't"); $g1->add_edge_by_id("I", "apple", "eat"); my $g2 = Graph->new(multiedged => 1); $g2->add_vertices("she","cake","apple juice","swim"); $g2->add_edge_by_id("she", "apple juice", "drink"); $g2->add_edge_by_id("she", "swim", "can"); $g2->add_edge_by_id("she", "cake", "eat"); my $s = new Graph::Similarity(graph => [$g1,$g2]); my $method = $s->use('SimimilarityFlooding'); $method->calculate(); $method->showAllSimilarities;
Graph is composed of vertices and edges (This is often also referred as nodes/edge in network). Graph::Similarity calculate the similarity of the vertices(nodes) by the following algorithms,
The algorithm is implemented by referring to the above papers. Each module in implementation layer(Graph::Similarity::<algorithm>) explains briefly about the algorithm. However, if you would like to know the details, please read the original papers.
Constructor. Create instance with Graph argument. SimRank is one Graph, the others need two Graphs for the algorithm.
$algorithm is either 'SimRank', 'CoupledNodeEdgeScoring' or 'SimilarityFlooding' Return an object of method.
This use method verifies Graph feature to see whether it fits to the requirement. If there is no required feature, it dies out. For example, when you specify two Graph in SimRank, it dies because SimRank needs to be calculated from one graph.
Using the method that is specified by use(), calculate the similarity. This returns a hash reference which is the results of calculation.
Set the number of Iteration. The argument should be Integer.
The results to STDOUT.
The vertex(node) has the name when it's created by Graph Module. Say, if you want to know the similarity between vertex "X" and "Y", use this method.
As an example of SimRank, we use Fig1 in the paper.
use Graph; use Graph::Similarity; my $g = Graph->new; $g->add_vertices("Univ","ProfA","StudentA","ProfB","StudentB"); $g->add_edges(['Univ', 'ProfA'], ['ProfA', 'StudentA'], ['StudentA', 'Univ'], ['Univ', 'ProfB'], ['ProfB', 'StudentB'], ['StudentB', 'ProfB']); my $s = new Graph::Similarity(graph => [$g]); my $method = $s->use('SimRank'); $method->setNumOfIteration(5); $method->setConst(0.8); my $result = $method->calculate(); # print Dumper $result $method->showAllSimilarities();
The result is as follows. The number is very close to the Fig 1.
StudentA - StudentA : 1 StudentA - ProfA : 0 StudentA - StudentB : 0.33048576 StudentA - Univ : 0 StudentA - ProfB : 0.04096 ProfA - StudentA : 0 ProfA - ProfA : 1 ProfA - StudentB : 0.1024 ProfA - Univ : 0 ProfA - ProfB : 0.4131072 StudentB - StudentA : 0.33048576 StudentB - ProfA : 0.1024 StudentB - StudentB : 1 StudentB - Univ : 0.032768 StudentB - ProfB : 0.08445952 Univ - StudentA : 0 Univ - ProfA : 0 Univ - StudentB : 0.032768 Univ - Univ : 1 Univ - ProfB : 0.128 ProfB - StudentA : 0.04096 ProfB - ProfA : 0.4131072 ProfB - StudentB : 0.084983808 ProfB - Univ : 0.132194304 ProfB - ProfB : 1
As an example, use Fig 3 in the papaer.
use Graph; use Graph::Similarity; my $g1 = Graph->new(multiedged => 1); $g1->add_vertices("a","a1","a2"); $g1->add_edge_by_id("a", "a1", "l1"); $g1->add_edge_by_id("a", "a2", "l1"); $g1->add_edge_by_id("a1", "a2", "l2"); my $g2 = Graph->new(multiedged => 1); $g2->add_vertices("b","b1","b2"); $g2->add_edge_by_id("b", "b1", "l1"); $g2->add_edge_by_id("b", "b2", "l2"); $g2->add_edge_by_id("b2", "b1", "l2"); my $s = new Graph::Similarity(graph => [$g1,$g2]); my $method = $s->use('SimilarityFlooding'); $method->setNumOfIteration(5); my $result = $method->calculate(); # print Dumper $result $method->showAllSimilarities();
The result is the below. The edit distance is not used in the paper, whereas we use edit distance as initial value. This causes the slight difference.
a2 - b : 0.000115041702617199 a2 - b1 : 0.917094477998274 a2 - b2 : 0.191429393155019 a - b : 1 a - b1 : 0.000115041702617199 a - b2 : 0.000115041702617199 a1 - b : 0.191429393155019 a1 - b1 : 0.385493960310613 a1 - b2 : 0.699762726488352
Fig 1.2 in the paper, "Measure of Similarity between Graph Vertices: Applications to Synonym Extraction and Web Searching", as an example.
use Graph; use Graph::Similarity; my $g1 = Graph->new(); $g1->add_vertices("a1","a2","a3","a4"); $g1->add_edges(["a1","a3"],["a1","a2"],["a2","a1"],["a2","a3"], ["a3","a2"],["a4","a1"],["a4","a3"]); my $g2 = Graph->new(); $g2->add_vertices("b1","b2","b3","b4","b5","b6"); $g2->add_edges(["b1","b3"],["b3","b1"],["b6","b1"],["b6","b3"], ["b3","b6"],["b3","b5"],["b2","b6"],["b2","b4"], ["b1","b4"],["b6","b4"]); my $s = new Graph::Similarity(graph => [$g1,$g2]); my $method = $s->use('CoupledNodeEdgeScoring'); $method->setNumOfIteration(50); my $result = $method->calculate(); # print Dumper $result $method->showAllSimilarities();
The result is,
b3 - a2 : 0.311518652195988 b3 - a4 : 0.166703492014422 b3 - a1 : 0.290390588307599 b3 - a3 : 0.282452510821415 b6 - a2 : 0.301149501715672 b6 - a4 : 0.199935544942559 b6 - a1 : 0.30383446637482 b6 - a3 : 0.253224302437108 b1 - a2 : 0.278635459119205 b1 - a4 : 0.128928289895856 b1 - a1 : 0.263618445136368 b1 - a3 : 0.272302658479426 b5 - a2 : 0.0758992640884854 b5 - a4 : 0 b5 - a1 : 0.0633623885302286 b5 - a3 : 0.101837901214133 b2 - a2 : 0.126836930942235 b2 - a4 : 0.126836930942235 b2 - a1 : 0.128617950209435 b2 - a3 : 0.0624424971383059 b4 - a2 : 0.170129852866194 b4 - a4 : 0 b4 - a1 : 0.15400277534204 b4 - a3 : 0.246229188289944
You may see the following error messages:
This algorithm can only apply to single graph
The algorithm needs to have single graph as argument.
The graph needs to be directed graph
Undirected graph can't be applied to this algorithm.
The graph needs to be multiedged
The algorithm needs to has multiedged graph with Graph->new(multiedged => 1)
Graph::Similarity requires no configuration files or environment variables.
None.
Shohei Kameda <shoheik@cpan.org>
Copyright (c) 2012, Shohei Kameda <shoheik@cpan.org>
. All rights reserved.
This module is free software; you can redistribute it and/or modify it under the same terms as Perl itself. See perlartistic.
BECAUSE THIS SOFTWARE IS LICENSED FREE OF CHARGE, THERE IS NO WARRANTY FOR THE SOFTWARE, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES PROVIDE THE SOFTWARE "AS IS" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE SOFTWARE IS WITH YOU. SHOULD THE SOFTWARE PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR, OR CORRECTION.
IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR REDISTRIBUTE THE SOFTWARE AS PERMITTED BY THE ABOVE LICENCE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL, OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE SOFTWARE (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE SOFTWARE TO OPERATE WITH ANY OTHER SOFTWARE), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES.