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Model-based clustering for random hypergraphs

Author

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  • Tin Lok James Ng

    (Trinity College Dublin)

  • Thomas Brendan Murphy

    (University College Dublin)

Abstract

A probabilistic model for random hypergraphs is introduced to represent unary, binary and higher order interactions among objects in real-world problems. This model is an extension of the latent class analysis model that introduces two clustering structures for hyperedges and captures variation in the size of hyperedges. An expectation maximization algorithm with minorization maximization steps is developed to perform parameter estimation. Model selection using Bayesian Information Criterion is proposed. The model is applied to simulated data and two real-world data sets where interesting results are obtained.

Suggested Citation

  • Tin Lok James Ng & Thomas Brendan Murphy, 2022. "Model-based clustering for random hypergraphs," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(3), pages 691-723, September.
    • Handle: RePEc:spr:advdac:v:16:y:2022:i:3:d:10.1007_s11634-021-00454-7
    DOI: 10.1007/s11634-021-00454-7
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    References listed on IDEAS

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    1. Simón Lunagómez & Sayan Mukherjee & Robert L. Wolpert & Edoardo M. Airoldi, 2017. "Geometric Representations of Random Hypergraphs," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 363-383, January.
    2. Hoff P.D. & Raftery A.E. & Handcock M.S., 2002. "Latent Space Approaches to Social Network Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1090-1098, December.
    3. Mark S. Handcock & Adrian E. Raftery & Jeremy M. Tantrum, 2007. "Model‐based clustering for social networks," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 170(2), pages 301-354, March.
    4. Gilles Celeux & Gérard Govaert, 1991. "Clustering criteria for discrete data and latent class models," Journal of Classification, Springer;The Classification Society, vol. 8(2), pages 157-176, December.
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