Multimodal Clustering for Community Detection

Multimodal clustering is an unsupervised technique for mining interesting patterns in n-adic binary relations or n-mode networks. Among different types of such generalized patterns one can find biclusters and formal concepts (maximal bicliques) for 2-mode case, triclusters and triconcepts for 3-mode case, closed nsets for n-mode case, etc. Object-attribute biclustering (OA-biclustering) for mining large binary datatables (formal contexts or 2-mode networks) arose by the end of the last decade due to intractability of computation problems related to formal concepts; this type of patterns was proposed as a meaningful and scalable approximation of formal concepts. In this paper, our aim is to present recent advance in OAbiclustering and its extensions to mining multi-mode communities in SNA setting. We also discuss connection between clustering coefficients known in SNA community for 1-mode and 2-mode networks and OA-bicluster density, the main quality measure of an OA-bicluster. Our experiments with 2-, 3-, and 4-mode large realworld networks show that this type of patterns is suitable for community detection in multi-mode cases within reasonable time even though the number of corresponding n-cliques is still unknown due to computation difficulties. An interpretation of OA-biclusters for 1-mode networks is provided as well. Dmitry I. Ignatov 1National Research University Higher School of Economics, Moscow, Russia, e-mail: [email protected] Alexander Semenov 1National Research University Higher School of Economics, Moscow, Russia, and 2Mobile TeleSystems PJSC, Moscow, Russia, e-mail: [email protected] Daria Komissarova 1National Research University Higher School of Economics, Moscow, Russia, e-mail: [email protected] Dmitry V. Gnatyshak 1National Research University Higher School of Economics, Moscow, Russia,, e-mail: [email protected] 1 ar X iv :1 70 2. 08 55 7v 1 [ cs .S I] 2 7 Fe b 20 17 2 Dmitry I. Ignatov, Alexander Semenov, Daria Komissarova, and Dmitry V. Gnatyshak