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Summable and nonsummable data-driven models for community detection in feature-rich networks

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Abstract

A feature-rich network is a network whose nodes are characterized by categorical or quantitative features. We propose a data-driven model for finding a partition of the nodes to approximate both the network link data and the feature data. The model involves summary quantitative characteristics of both network links and features. We distinguish between two modes of using the network link data. One mode postulates that the link values are comparable and summable across the network (summability); the other assumption models the case in which different nodes represent different measurement systems so that the link data are neither comparable, nor summable, across different nodes (nonsummability). We derive a Pythagorean decomposition of the combined data scatter involving our data recovery least-squares criterion. We address an equivalent problem of maximizing its complementary part, the contribution of a found partition to the combined data scatter. We follow a doubly greedy strategy in maximizing that. First, communities are found one-by-one, and second, entities are added one-by-one in the process of identifying a community. Our algorithms determine the number of clusters automatically. The nonsummability version proves to have a niche of its own; also, it is faster than the other version. In our experiments, they appear to be competitive over generated synthetic data sets and six real-world data sets from the literature.

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Acknowledgements

This article was prepared within the framework of the HSE University Basic Research Program. The authors are indebted to the anonymous referees for their invaluable comments taken into account in the final draft.

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Authors and Affiliations

  1. Department of Data Analysis and Artificial Intelligence, HSE University, Pokrovsky Boulevard, 11, Moscow, Russian Federation

    Soroosh Shalileh & Boris Mirkin

  2. Laboratory of Methods for Big Data Analysis, HSE University, Pokrovsky Boulevard, 11, Moscow, Russian Federation

    Soroosh Shalileh

  3. Department of Computer Science and Information Systems, Birkbeck University of London, Malet Street, London, WC1E 7HX, UK

    Boris Mirkin

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  1. Soroosh Shalileh
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Correspondence to Boris Mirkin.

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Shalileh, S., Mirkin, B. Summable and nonsummable data-driven models for community detection in feature-rich networks. Soc. Netw. Anal. Min. 11, 67 (2021). https://doi.org/10.1007/s13278-021-00774-8

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