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Fast and consistent algorithm for the latent block model

Author

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  • Vincent Brault

    (Univ. Grenoble Alpes, CNRS, Grenoble INP, LJK)

  • Antoine Channarond

    (Université de Rouen Normandie)

Abstract

The latent block model is used to simultaneously rank the rows and columns of a matrix to reveal a block structure. The algorithms used for estimation are often time consuming. However, recent work shows that the log-likelihood ratios are equivalent under the complete and observed (with unknown labels) models and the groups posterior distribution to converge as the size of the data increases to a Dirac mass located at the actual groups configuration. Based on these observations, the algorithm Largest Gaps is proposed in this paper to perform clustering using only the marginals of the matrix, when the number of blocks is very small with respect to the size of the whole matrix in the case of binary data. In addition, a model selection method is incorporated with a proof of its consistency. Thus, this paper shows that studying simplistic configurations (few blocks compared to the size of the matrix or very contrasting blocks) with complex algorithms is useless since the marginals already give very good parameter and classification estimates.

Suggested Citation

  • Vincent Brault & Antoine Channarond, 2024. "Fast and consistent algorithm for the latent block model," Computational Statistics, Springer, vol. 39(3), pages 1621-1657, May.
    • Handle: RePEc:spr:compst:v:39:y:2024:i:3:d:10.1007_s00180-023-01373-1
    DOI: 10.1007/s00180-023-01373-1
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    References listed on IDEAS

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    1. Maria Iannario, 2010. "On the identifiability of a mixture model for ordinal data," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 87-94.
    2. Timothée Tabouy & Pierre Barbillon & Julien Chiquet, 2020. "Variational Inference for Stochastic Block Models From Sampled Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(529), pages 455-466, January.
    3. Bhatia, Parmeet Singh & Iovleff, Serge & Govaert, Gérard, 2017. "blockcluster: An R Package for Model-Based Co-Clustering," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 76(i09).
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