Clustering bipartite graphs in terms of approximate formal concepts and sub-contexts

Bruno Gaume (1, 2) , Emmanuel Navarro (2) , Henri Prade (3)

1 CLLE-ERSS - Cognition, Langues, Langage, Ergonomie
2 IRIT - Institut de recherche en informatique de Toulouse
3 IRIT-ADRIA - Argumentation, Décision, Raisonnement, Incertitude et Apprentissage

The paper first offers a parallel between two approaches to conceptual clustering, namely formal conceptanalysis (augmented with the introduction of new operators) and bipartite graph analysis. It is shown that aformal concept (as defined in formal concept analysis) corresponds to the idea of a maximal bi-clique, whilesub-contexts, which correspond to independent “conceptual worlds” that can be characterized by means ofthe new operators introduced, are disconnected sub-graphs in a bipartite graph. The parallel between formalconcept analysis and bipartite graph analysis is further exploited by considering “approximation” methodson both sides. It leads to suggest new ideas for providing simplified views of datasets, taking also inspirationfrom the search for approximate item sets in data mining, and the detection of communities in hierarchicalsmall worlds.

Mots clés: formal concept analysis (FCA); bipartite graph; small world; clustering; possibility theory

Domaines: Intelligence artificielle [cs.AI]

Bruno Gaume, Emmanuel Navarro, Henri Prade. Clustering bipartite graphs in terms of approximate formal concepts and sub-contexts. International Journal of Computational Intelligence Systems, 2013, pp.1125--1142. ⟨hal-00992119v1⟩