Model-based clustering and classification with non-normal mixture distributions

Lee, Sharon X. and McLachlan, Geoffrey J. (2013) Model-based clustering and classification with non-normal mixture distributions. Statistical Methods and Applications, 22 4: 427-454. doi:10.1007/s10260-013-0237-4


Author Lee, Sharon X.
McLachlan, Geoffrey J.
Title Model-based clustering and classification with non-normal mixture distributions
Journal name Statistical Methods and Applications   Check publisher's open access policy
ISSN 1618-2510
1613-981X
Publication date 2013-11-01
Year available 2013
Sub-type Article (original research)
DOI 10.1007/s10260-013-0237-4
Open Access Status Not yet assessed
Volume 22
Issue 4
Start page 427
End page 454
Total pages 28
Place of publication Heidelberg, Germany
Publisher Springer
Language eng
Abstract Non-normal mixture distributions have received increasing attention in recent years. Finite mixtures of multivariate skew-symmetric distributions, in particular, the skew normal and skew -mixture models, are emerging as promising extensions to the traditional normal and -mixture models. Most of these parametric families of skew distributions are closely related, and can be classified into four forms under a recently proposed scheme, namely, the restricted, unrestricted, extended, and generalised forms. In this paper, we consider some of these existing proposals of multivariate non-normal mixture models and illustrate their practical use in several real applications. We first discuss the characterizations along with a brief account of some distributions belonging to the above classification scheme, then references for software implementation of EM-type algorithms for the estimation of the model parameters are given. We then compare the relative performance of restricted and unrestricted skew mixture models in clustering, discriminant analysis, and density estimation on six real datasets from flow cytometry, finance, and image analysis. We also compare the performance of mixtures of skew normal and -component distributions with other non-normal component distributions, including mixtures with multivariate normal-inverse-Gaussian distributions, shifted asymmetric Laplace distributions and generalized hyperbolic distributions.
Formatted abstract
Non-normal mixture distributions have received increasing attention in recent years. Finite mixtures of multivariate skew-symmetric distributions, in particular, the skew normal and skew t-mixture models, are emerging as promising extensions to the traditional normal and t-mixture models. Most of these parametric families of skew distributions are closely related, and can be classified into four forms under a recently proposed scheme, namely, the restricted, unrestricted, extended, and generalised forms. In this paper, we consider some of these existing proposals of multivariate non-normal mixture models and illustrate their practical use in several real applications. We first discuss the characterizations along with a brief account of some distributions belonging to the above classification scheme, then references for software implementation of EM-type algorithms for the estimation of the model parameters are given. We then compare the relative performance of restricted and unrestricted skew mixture models in clustering, discriminant analysis, and density estimation on six real datasets from flow cytometry, finance, and image analysis. We also compare the performance of mixtures of skew normal and t-component distributions with other non-normal component distributions, including mixtures with multivariate normal-inverse-Gaussian distributions, shifted asymmetric Laplace distributions and generalized hyperbolic distributions.
Keyword EM algorithm
Mixture models
Multivariate skew normal distribution
Multivariate skew t-distribution
Skew distributions
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2014 Collection
 
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