Parsimonious mixtures of multivariate contaminated normal distributions

A mixture of multivariate contaminated normal distributions is developed for model‐based clustering. In addition to the parameters of the classical normal mixture, our contaminated mixture has, for each cluster, a parameter controlling the proportion of mild outliers and one specifying the degree of...

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Bibliographic Details
Published in:Biometrical journal Vol. 58; no. 6; pp. 1506 - 1537
Main Authors: Punzo, Antonio, McNicholas, Paul D.
Format: Journal Article
Language:English
Published: Germany Blackwell Publishing Ltd 01.11.2016
Wiley - VCH Verlag GmbH & Co. KGaA
Subjects:
Algorithms
Cluster Analysis
Contaminated normal distribution
Contamination
EM algorithm
Mixture models
Model-based clustering
Models, Statistical
Normal Distribution
Contaminated normal distribution
EM algorithm
Contamination
Mixture models
Model-based clustering
ISSN:0323-3847, 1521-4036, 1521-4036
Online Access:Get full text
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Summary:A mixture of multivariate contaminated normal distributions is developed for model‐based clustering. In addition to the parameters of the classical normal mixture, our contaminated mixture has, for each cluster, a parameter controlling the proportion of mild outliers and one specifying the degree of contamination. Crucially, these parameters do not have to be specified a priori, adding a flexibility to our approach. Parsimony is introduced via eigen‐decomposition of the component covariance matrices, and sufficient conditions for the identifiability of all the members of the resulting family are provided. An expectation‐conditional maximization algorithm is outlined for parameter estimation and various implementation issues are discussed. Using a large‐scale simulation study, the behavior of the proposed approach is investigated and comparison with well‐established finite mixtures is provided. The performance of this novel family of models is also illustrated on artificial and real data.
Bibliography:istex:F803EB533857CE9AC12ADC40DE9A62BAB05C1F5C
ark:/67375/WNG-KJH5QNT0-T
ArticleID:BIMJ1713
Supporting Information
Italian Government - No. RBFR12SHVV
Canada Research Chairs program
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
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ISSN:0323-3847
1521-4036
1521-4036
DOI:10.1002/bimj.201500144