On closure operators related to maximal tricliques in tripartite hypergraphs

Ignatov, Dmitry I.

doi:10.1016/j.dam.2017.12.032

Cited by 2 publications

(2 citation statements)

References 22 publications

(44 reference statements)

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“…It is possible to mine maximal closed and connected subgraphs in them and interpret them as communities [59]; these patterns coincide with bicliques and formal concepts in two-mode case. However, for higher dimensions such n-partite graphs are not equivalent to n-adic contexts and may result in information loss or phantom hyperedges if we reduce the latter to the former or vice versa [34]. In [29], for analysing such tripartite network composed by two two-mode networks with one shared part, biclusters from these two networks have been used.…”

Section: Related Workmentioning

confidence: 99%

Multimodal Clustering for Community Detection

Ignatov

Semenov

Komissarova

et al. 2017

Formal Concept Analysis of Social Networks

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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.

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Section: Related Workmentioning

confidence: 99%

Multimodal Clustering for Community Detection

Ignatov

Semenov

Komissarova

et al. 2017

Formal Concept Analysis of Social Networks

Self Cite

View full text Add to dashboard Cite

show abstract

“…Such hypergraphs correspond to 3-dimensional Boolean datasets, e.g. data describing objects by sets of attributes under different conditions (not to be mistaken for the notion of condition used in Section 3), and the enumeration of their minimal transversals is involved in the mining of different patterns such as triadic concepts Ignatov et al (2015); Ignatov (2018), implications Ryssel et al (2014); Sertkaya (2009) and association rules Missaoui and Kwuida (2011). This work comes from an interest in bounding the number of triadic concepts as studied in triadic concept analysis Lehmann and Wille (1995).…”

Section: Introductionmentioning

confidence: 99%