Graph recognition by seriation and frequent substructures mining

Many interesting applications of Pattern Recognition techniques can take advantage in dealing with labeled graphs as input patterns. To this aim the most important issue is the definition of a dissimilarity measure between graphs. In this paper we propose a representation technique able to characterize the input graphs as real valued feature vectors, allowing the use of standard classification systems. This procedure consists in two distinct stages. In the first step a labeled graph is transformed into a sequence of its vertices, ordered according to a given criterion. In a second step this sequence is mapped into a real valued vector. To perform the latter stage, we propose a novel Granular Computing procedure searching for frequent substructures, called GRADIS. This algorithm is in charge of the inexact substructures identification and of the embedding of the sequenced graphs using the symbolic histogram approach. Tests have been performed by synthetically generating a set of graph classification problem instances with the aim to measure system performances when dealing with different types of graphs, as well when increasing problem hardness.