Exact Median Graph Computation Via Graph Embedding

Authors:
Miquel Ferrer;Ernest Valveny;Francesc Serratosa;Horst Bunke
Affiliations:
Centre de Visió per Computador, Dep. Ciències de la Computació, Universitat Autònoma de Barcelona, Bellaterra, Spain 08193;Centre de Visió per Computador, Dep. Ciències de la Computació, Universitat Autònoma de Barcelona, Bellaterra, Spain 08193;Departament d'Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, Tarragona, Spain 43007;Department of Computer Science and Applied Mathematics, University of Bern, Bern, Switzerland CH3012
Venue:
SSPR & SPR '08 Proceedings of the 2008 Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition
Year:
2008

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Abstract

Given a set of graphs, the median graph is defined as the graph which has the smallest sum of distances (SOD) to all the graphs in the set. It has been proposed as a tool to obtain the representative of such a set. In spite of its potential applications, the existing algorithms are computationally complex and have a very limited applicability. In this paper we propose a new approach for the exact computation of the median graph based on graph embedding in vector spaces. Graphs are embedded into a vector space and the median is computed in the vector domain. After that, the median graph is recovered from this median vector. Experiments on a synthetic database show that our approach outperforms the previous existing exact algorithms both on computation time and number of SOD computations.