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Open AccessArticle

Multi-Partitions Subspace Clustering

1
Biostatistics Department, Univ. Lille, CHU Lille, ULR 2694—METRICS: Évaluation des Technologies de Santé et des Pratiques MéDicales, F-59000 Lille, France
2
Inria Lille—Nord Europe, 59650 Villeneuve d’Ascq, France
Mathematics 2020, 8(4), 597; https://doi.org/10.3390/math8040597
Received: 28 February 2020 / Revised: 6 April 2020 / Accepted: 10 April 2020 / Published: 15 April 2020
(This article belongs to the Special Issue Probability, Statistics and Their Applications)
In model based clustering, it is often supposed that only one clustering latent variable explains the heterogeneity of the whole dataset. However, in many cases several latent variables could explain the heterogeneity of the data at hand. Finding such class variables could result in a richer interpretation of the data. In the continuous data setting, a multi-partition model based clustering is proposed. It assumes the existence of several latent clustering variables, each one explaining the heterogeneity of the data with respect to some clustering subspace. It allows to simultaneously find the multi-partitions and the related subspaces. Parameters of the model are estimated through an EM algorithm relying on a probabilistic reinterpretation of the factorial discriminant analysis. A model choice strategy relying on the BIC criterion is proposed to select to number of subspaces and the number of clusters by subspace. The obtained results are thus several projections of the data, each one conveying its own clustering of the data. Model’s behavior is illustrated on simulated and real data. View Full-Text
Keywords: clustering; mixture model; factorial discriminant analysis; EM algorithm clustering; mixture model; factorial discriminant analysis; EM algorithm
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Vandewalle, V. Multi-Partitions Subspace Clustering. Mathematics 2020, 8, 597.

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