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Model-based clustering using copulas with applications

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Kosmidis, Ioannis and Karlis, Dimitris (2016) Model-based clustering using copulas with applications. Statistics and Computing, 26 (5). pp. 1079-1099. doi:10.1007/s11222-015-9590-5

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Official URL: https://doi.org/10.1007/s11222-015-9590-5

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Abstract

The majority of model-based clustering techniques is based on multivariate normal models and their variants. In this paper copulas are used for the construction of flexible families of models for clustering applications. The use of copulas in model-based clustering offers two direct advantages over current methods: (i) the appropriate choice of copulas provides the ability to obtain a range of exotic shapes for the clusters, and (ii) the explicit choice of marginal distributions for the clusters allows the modelling of multivariate data of various modes (either discrete or continuous) in a natural way. This paper introduces and studies the framework of copula-based finite mixture models for clustering applications. Estimation in the general case can be performed using standard EM, and, depending on the mode of the data, more efficient procedures are provided that can fully exploit the copula structure. The closure properties of the mixture models under marginalization are discussed, and for continuous, real-valued data parametric rotations in the sample space are introduced, with a parallel discussion on parameter identifiability depending on the choice of copulas for the components. The exposition of the methodology is accompanied and motivated by the analysis of real and artificial data.

Item Type: Journal Article
Subjects: H Social Sciences > HA Statistics
Divisions: Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH): Cluster analysis, Multivariate analysis, Copulas (Mathematical statistics), Dependence (Statistics)
Journal or Publication Title: Statistics and Computing
Publisher: Springer
ISSN: 0960-3174
Official Date: September 2016
Dates:
DateEvent
September 2016Published
23 June 2015Accepted
Volume: 26
Number: 5
Page Range: pp. 1079-1099
DOI: 10.1007/s11222-015-9590-5
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Open Access

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