PT Journal
AU Miquel Ferrer
   Ernest Valveny
   F. Serratosa
   K. Riesen
   Horst Bunke
TI Generalized Median Graph Computation by Means of Graph Embedding in Vector Spaces
SO Pattern Recognition
JI PR
PY 2010
BP 1642–1655
VL 43
IS 4
DI 10.1016/j.patcog.2009.10.013
DE Graph matching; Weighted mean of graphs; Median graph; Graph embedding; Vector spaces
AB The median graph has been presented as a useful tool to represent a set of graphs. Nevertheless its computation is very complex and the existing algorithms are restricted to use limited amount of data. In this paper we propose a new approach for the computation of the median graph based on graph embedding. Graphs are embedded into a vector space and the median is computed in the vector domain. We have designed a procedure based on the weighted mean of a pair of graphs to go from the vector domain back to the graph domain in order to obtain a final approximation of the median graph. Experiments on three different databases containing large graphs show that we succeed to compute good approximations of the median graph. We have also applied the median graph to perform some basic classification tasks achieving reasonable good results. These experiments on real data open the door to the application of the median graph to a number of more complex machine learning algorithms where a representative of a set of graphs is needed.
ER