Statistics and Computing

, Volume 26, Issue 5, pp 1079–1099 | Cite as

Model-based clustering using copulas with applications

  • Ioannis Kosmidis
  • Dimitris Karlis


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.


Mixture models Dependence modelling Parametric rotations Multivariate discrete data  Mixed-domain data 

Supplementary material

11222_2015_9590_MOESM1_ESM.pdf (96 kb)
Supplementary material extends Example 4.2 to illustrate that distinct sensible, transformations can lead to different results. R scripts that reproduce the analyses undertaken in this paper are available upon request to the authors.(PDF 96.5KB)


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Statistical ScienceUniversity College LondonLondonUK
  2. 2.Department of StatisticsAthens University of Economics and BusinessAthensGreece

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