Abstract and Local Concepts in Attributed Networks

and Local Concepts in Attributed Networks Henry Soldano, Guillaume Santini, and Dominique Bouthinon 1 Université Paris 13, Sorbonne Paris Cité, L.I.P.N UMR-CNRS 7030 F-93430, Villetaneuse, France 2 Atelier de BioInformatique, ISYEB UMR 7205 CNRS MNHN UPMC EPHE, Museum National d’Histoire Naturelle, F-75005, Paris, France Abstract. We consider attribute pattern mining in attributed graphs through recent developments of Formal Concept Analysis. The corresponding methods restrain the extensional space 2 , i.e. the space of possible pattern extensions in the object set O, to a subset satisfying structural properties. When considering an attributed graph, we consider its vertices as the objects under study, each described in a pattern language, as 2 where I is an attribute set. The restriction of the extensional space depends then on the graph topology. We consider two levels. At the global level, the core idea is to reduce the extension of each pattern in such a way that the corresponding abstract extension induces a subgraph made of dense parts whose nodes satisfy some connectivity property. At the local level a pattern has various extensions each associated to one dense part. We obtain that way abstract closed patterns and local closed patterns, together with abstract and local implication rules. Overall, we propose here a way to extract information associated to the attributes labelling the graph vertices, according to its topology. We consider in particular the detection of communities in subgraphs of an attributed network associated to local closed patterns and local implications. We consider attribute pattern mining in attributed graphs through recent developments of Formal Concept Analysis. The corresponding methods restrain the extensional space 2 , i.e. the space of possible pattern extensions in the object set O, to a subset satisfying structural properties. When considering an attributed graph, we consider its vertices as the objects under study, each described in a pattern language, as 2 where I is an attribute set. The restriction of the extensional space depends then on the graph topology. We consider two levels. At the global level, the core idea is to reduce the extension of each pattern in such a way that the corresponding abstract extension induces a subgraph made of dense parts whose nodes satisfy some connectivity property. At the local level a pattern has various extensions each associated to one dense part. We obtain that way abstract closed patterns and local closed patterns, together with abstract and local implication rules. Overall, we propose here a way to extract information associated to the attributes labelling the graph vertices, according to its topology. We consider in particular the detection of communities in subgraphs of an attributed network associated to local closed patterns and local implications.