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Model-based clustering using copulas with applications

Kosmidis, I; Karlis, D; (2016) Model-based clustering using copulas with applications. Statistics and Computing , 26 (5) pp. 1079-1099. 10.1007/s11222-015-9590-5. Green open access

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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 (discrete, continuous, both discrete and 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.

Type: Article
Title: Model-based clustering using copulas with applications
Open access status: An open access version is available from UCL Discovery
DOI: 10.1007/s11222-015-9590-5
Publisher version: http://dx.doi.org/10.1007/s11222-015-9590-5
Language: English
Additional information: The final publication is available at Springer via http://dx.doi.org/10.​1007/​s11222-015-9590-5.
Keywords: Mixture models, Dependence modelling, Parametric rotations, Multivariate discrete data, Mixed-domain data
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
URI: https://discovery.ucl.ac.uk/id/eprint/1433312
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