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Probabilistic Community Detection With Unknown Number of Communities

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  • Junxian Geng
  • Anirban Bhattacharya
  • Debdeep Pati

Abstract

A fundamental problem in network analysis is clustering the nodes into groups which share a similar connectivity pattern. Existing algorithms for community detection assume the knowledge of the number of clusters or estimate it a priori using various selection criteria and subsequently estimate the community structure. Ignoring the uncertainty in the first stage may lead to erroneous clustering, particularly when the community structure is vague. We instead propose a coherent probabilistic framework for simultaneous estimation of the number of communities and the community structure, adapting recently developed Bayesian nonparametric techniques to network models. An efficient Markov chain Monte Carlo (MCMC) algorithm is proposed which obviates the need to perform reversible jump MCMC on the number of clusters. The methodology is shown to outperform recently developed community detection algorithms in a variety of synthetic data examples and in benchmark real-datasets. Using an appropriate metric on the space of all configurations, we develop nonasymptotic Bayes risk bounds even when the number of clusters is unknown. Enroute, we develop concentration properties of nonlinear functions of Bernoulli random variables, which may be of independent interest in analysis of related models. Supplementary materials for this article are available online.

Suggested Citation

  • Junxian Geng & Anirban Bhattacharya & Debdeep Pati, 2019. "Probabilistic Community Detection With Unknown Number of Communities," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(526), pages 893-905, April.
  • Handle: RePEc:taf:jnlasa:v:114:y:2019:i:526:p:893-905
    DOI: 10.1080/01621459.2018.1458618
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    Cited by:

    1. Sadick Mohammed & Awudu Abdulai, 2022. "Do Egocentric information networks influence technical efficiency of farmers? Empirical evidence from Ghana," Journal of Productivity Analysis, Springer, vol. 58(2), pages 109-128, December.
    2. Sirio Legramanti & Tommaso Rigon & Daniele Durante, 2022. "Bayesian Testing for Exogenous Partition Structures in Stochastic Block Models," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(1), pages 108-126, June.
    3. Florian Huber & Gary Koop & Massimiliano Marcellino & Tobias Scheckel, 2024. "Bayesian modelling of VAR precision matrices using stochastic block networks," Papers 2407.16349, arXiv.org.
    4. Ludkin, Matthew, 2020. "Inference for a generalised stochastic block model with unknown number of blocks and non-conjugate edge models," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    5. Heather Mathews & Alexander Volfovsky, 2023. "Community informed experimental design," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(4), pages 1141-1166, October.

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