Fast and consistent algorithm for the latent block model

• Published in: Computational statistics Vol. 39; no. 3; pp. 1621 - 1657
• Main Authors: Brault, Vincent, Channarond, Antoine
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.05.2024; Springer Nature B.V; Springer Verlag
• Subjects: Algorithms; Binary data; Clustering; Configurations; Economic Theory/Quantitative Economics/Mathematical Methods; Likelihood ratio; Mathematics and Statistics; Matrix algebra; Original Paper; Probability and Statistics in Computer Science; Probability Theory and Stochastic Processes; Statistics; Statistics Theory; Data analysis; Latent block model; Largest Gaps algorithm; Model selection; Sélection de modèle; Modèle des blocs latents; Largest Gaps Algorithm; Model Selection; Algorithme Largest Gaps; Latent Block Model
• ISSN: 0943-4062; 1613-9658
• DOI: 10.1007/s00180-023-01373-1

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.