Hierarchical clustering with discrete latent variable models and the integrated classification likelihood

Etienne Côme (), Nicolas Jouvin (), Pierre Latouche () and Charles Bouveyron ()
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Etienne Côme: COSYS/GRETTIA, Université Gustave-Eiffel
Nicolas Jouvin: Université Paris 1 Panthéon-Sorbonne
Pierre Latouche: FP2M, CNRS FR 2036
Charles Bouveyron: Université Côte d’Azur, CNRS, Laboratoire J.A. Dieudonné

Advances in Data Analysis and Classification, 2021, vol. 15, issue 4, No 6, 957-986

Abstract: Abstract Finding a set of nested partitions of a dataset is useful to uncover relevant structure at different scales, and is often dealt with a data-dependent methodology. In this paper, we introduce a general two-step methodology for model-based hierarchical clustering. Considering the integrated classification likelihood criterion as an objective function, this work applies to every discrete latent variable models (DLVMs) where this quantity is tractable. The first step of the methodology involves maximizing the criterion with respect to the partition. Addressing the known problem of sub-optimal local maxima found by greedy hill climbing heuristics, we introduce a new hybrid algorithm based on a genetic algorithm which allows to efficiently explore the space of solutions. The resulting algorithm carefully combines and merges different solutions, and allows the joint inference of the number K of clusters as well as the clusters themselves. Starting from this natural partition, the second step of the methodology is based on a bottom-up greedy procedure to extract a hierarchy of clusters. In a Bayesian context, this is achieved by considering the Dirichlet cluster proportion prior parameter $$\alpha $$ α as a regularization term controlling the granularity of the clustering. A new approximation of the criterion is derived as a log-linear function of $$\alpha $$ α , enabling a simple functional form of the merge decision criterion. This second step allows the exploration of the clustering at coarser scales. The proposed approach is compared with existing strategies on simulated as well as real settings, and its results are shown to be particularly relevant. A reference implementation of this work is available in the R-package greed accompanying the paper.

Keywords: Mixture models; Block modeling; Co-clustering; Genetic algorithm; Model-based (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11634-021-00440-z

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