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A tractable Multi-Partitions Clustering

Matthieu Marbac 1, 2 Vincent Vandewalle 3, 4 
3 MODAL - MOdel for Data Analysis and Learning
LPP - Laboratoire Paul Painlevé - UMR 8524, Université de Lille, Sciences et Technologies, Inria Lille - Nord Europe, METRICS - Evaluation des technologies de santé et des pratiques médicales - ULR 2694, Polytech Lille - École polytechnique universitaire de Lille
Abstract : In the framework of model-based clustering, a model allowing several latent class variables is proposed. This model assumes that the distribution of the observed data can be factorized into several independent blocks of variables. Each block is assumed to follow a latent class model ({\it i.e.,} mixture with conditional independence assumption). The proposed model includes variable selection, as a special case, and is able to cope with the mixed-data setting. The simplicity of the model allows to estimate the repartition of the variables into blocks and the mixture parameters simultaneously, thus avoiding to run EM algorithms for each possible repartition of variables into blocks. For the proposed method, a model is defined by the number of blocks, the number of clusters inside each block and the repartition of variables into block. Model selection can be done with two information criteria, the BIC and the MICL, for which an efficient optimization is proposed. The performances of the model are investigated on simulated and real data. It is shown that the proposed method gives a rich interpretation of the dataset at hand ({\it i.e.,} analysis of the repartition of the variables into blocks and analysis of the clusters produced by each block of variables).
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Submitted on : Wednesday, January 24, 2018 - 12:11:57 AM
Last modification on : Saturday, June 25, 2022 - 7:26:58 PM

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Matthieu Marbac, Vincent Vandewalle. A tractable Multi-Partitions Clustering. Computational Statistics and Data Analysis, Elsevier, 2018, ⟨10.1016/j.csda.2018.06.013⟩. ⟨hal-01691417⟩



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