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

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

1 CLLE-LTC - 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 concept analysis (augmented with the introduction of new operators) and bipartite graph analysis. It is shown that a formal concept (as defined in formal concept analysis) corresponds to the idea of a maximal bi-clique, while sub-contexts, which correspond to independent “conceptual worlds” that can be characterized by means of the new operators introduced, are disconnected sub-graphs in a bipartite graph. The parallel between formal concept analysis and bipartite graph analysis is further exploited by considering “approximation” methods on both sides. It leads to suggest new ideas for providing simplified views of datasets, taking also inspiration from the search for approximate itemsets in data mining (with relaxed requirements), and the detection of communities in hierarchical small worlds.

Mots clés: Formal concept analysis (FCA); Bipartite graph; Small world; Clustering; Possibility theory

Domaines: Intelligence artificielle [cs.AI]; Apprentissage [cs.LG]; Logique en informatique [cs.LO]; Informatique et langage [cs.CL]

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, 6 (6), pp.1125-1142. ⟨10.1080/18756891.2013.819179⟩. ⟨hal-00992119v2⟩