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Multimodal Clustering for Community Detection

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Formal Concept Analysis of Social Networks

Part of the book series: Lecture Notes in Social Networks ((LNSN))

Abstract

Multimodal clustering is an unsupervised technique for mining interesting patterns in n-adic binary relations or n-mode networks. Among different types of such generalised patterns one can find biclusters and formal concepts (maximal bicliques) for two-mode case, triclusters and triconcepts for three-mode case, closed n-sets for n-mode case, etc. Object-attribute biclustering (OA-biclustering) for mining large binary datatables (formal contexts or two-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 OA-biclustering and its extensions to mining multi-mode communities in SNA setting. We also discuss connection between clustering coefficients known in SNA community for one-mode and two-mode networks and OA-bicluster density, the main quality measure of an OA-bicluster. Our experiments with two-, three-, and four-mode large real-world 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 one-mode networks is provided as well.

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Notes

  1. 1.

    www.https://en.wikipedia.org/wiki/Friend-to-friend.

  2. 2.

    We omit curly brackets here it what follows implying that {g}′ = g′ and {m}′ = m′.

  3. 3.

    Note that technically (g′, g′) is not an OA-bicluster since (g, g) ∉ I.

  4. 4.

    Here [⋅ ] means Iverson bracket defined as \([P] = \left \{\begin{array}{@{}l@{\quad }l@{}} 1\quad &\text{if }P\text{ is true;}\\ 0\quad &\text{otherwise,} \end{array} \right.\).

  5. 5.

    http://www.kde.cs.uni-kassel.de/bibsonomy/dumps/.

  6. 6.

    http://grouplens.org/datasets/movielens/.

  7. 7.

    There is a small inconsistency in the profiles of women w 14 (Helen) and w 15 (Dorothy), namely between their description in [22] and the downloaded dataset provided at https://networkdata.ics.uci.edu/netdata/html/davis.html, thus according to the latter e 12, e 13 ∈ w 14′ and e 11, e 9 ∈ w 15′.

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Acknowledgements

We would like to thank our colleagues Rakesh Agrawal, Loïc Cerf, Vincent Duquenne, Santo Fortunato, Bernhard Ganter, Jean-François Boulicaut, Mehdi Kaytoue, Boris Mirkin, Amedeo Napoli, Lhouri Nourine, Engelbert Mephu-Nguifo, Sergei Kuznetsov, Rokia Missaoui, Sergei Obiedkov, Camille Roth, Takeaki Uno, Stanley Wasserman, and Leonid Zhukov for their inspirational discussions or a piece of advice, which directly or implicitly influenced this study. We are grateful to our colleagues from the Laboratory for Internet Studies for their piece of advice as well. The study was implemented in the framework of the Basic Research Program at the National Research University Higher School of Economics in 2016 and 2017 and in the Laboratory of Intelligent Systems and Structural Analysis. The first author has also been supported by Russian Foundation for Basic Research.

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Authors and Affiliations

  1. National Research University Higher School of Economics, Moscow, Russia

    Dmitry I. Ignatov, Alexander Semenov, Daria Komissarova & Dmitry V. Gnatyshak

  2. Mobile TeleSystems PJSC, Moscow, Russia

    Alexander Semenov

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  1. Dmitry I. Ignatov
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  2. Alexander Semenov
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  3. Daria Komissarova
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  4. Dmitry V. Gnatyshak
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Correspondence to Dmitry I. Ignatov .

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Editors and Affiliations

  1. Department of Computer Science & Engineering, University of Quebec in Outaouais, Quebec, Canada

    Rokia Missaoui

  2. Faculty of Computer Science, National Research University Higher School of Economics, Moscow, Russia

    Sergei O. Kuznetsov

  3. Faculty of Computer Science, National Research University Higher School of Economics, Moscow, Russia

    Sergei Obiedkov

Appendix: Experiments with One-Mode Networks

Appendix: Experiments with One-Mode Networks

Table 9 Florentine family 1: 16×16, 58 edges
Full size table
Table 10 Florentine family 2: 16×16, 46 edges
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Table 11 Hi-tech: 36×36, 218 edges
Full size table
Table 12 Mexican people: 35×35, 268 edges
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Ignatov, D.I., Semenov, A., Komissarova, D., Gnatyshak, D.V. (2017). Multimodal Clustering for Community Detection. In: Missaoui, R., Kuznetsov, S., Obiedkov, S. (eds) Formal Concept Analysis of Social Networks. Lecture Notes in Social Networks. Springer, Cham. https://doi.org/10.1007/978-3-319-64167-6_4

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