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Model-based clustering via new parsimonious mixtures of heavy-tailed distributions

Author

Listed:
  • Salvatore D. Tomarchio

    (Università degli Studi di Catania)

  • Luca Bagnato

    (Università Cattolica del Sacro Cuore)

  • Antonio Punzo

    (Università degli Studi di Catania)

Abstract

Two families of parsimonious mixture models are introduced for model-based clustering. They are based on two multivariate distributions-the shifted exponential normal and the tail-inflated normal-recently introduced in the literature as heavy-tailed generalizations of the multivariate normal. Parsimony is attained by the eigen-decomposition of the component scale matrices, as well as by the imposition of a constraint on the tailedness parameters. Identifiability conditions are also provided. Two variants of the expectation-maximization algorithm are presented for maximum likelihood parameter estimation. Parameter recovery and clustering performance are investigated via a simulation study. Comparisons with the unconstrained mixture models are obtained as by-product. A further simulated analysis is conducted to assess how sensitive our and some well-established parsimonious competitors are to their own generative scheme. Lastly, our and the competing models are evaluated in terms of fitting and clustering on three real datasets.

Suggested Citation

  • Salvatore D. Tomarchio & Luca Bagnato & Antonio Punzo, 2022. "Model-based clustering via new parsimonious mixtures of heavy-tailed distributions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(2), pages 315-347, June.
    • Handle: RePEc:spr:alstar:v:106:y:2022:i:2:d:10.1007_s10182-021-00430-8
    DOI: 10.1007/s10182-021-00430-8
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    References listed on IDEAS

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    1. Hajo Holzmann & Axel Munk & Tilmann Gneiting, 2006. "Identifiability of Finite Mixtures of Elliptical Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(4), pages 753-763, December.
    2. Meng Li & Sijia Xiang & Weixin Yao, 2016. "Robust estimation of the number of components for mixtures of linear regression models," Computational Statistics, Springer, vol. 31(4), pages 1539-1555, December.
    3. repec:bla:biomet:v:71:y:2015:i:4:p:1081-1089 is not listed on IDEAS
    4. Antonio Punzo & Paul. D. McNicholas, 2017. "Robust Clustering in Regression Analysis via the Contaminated Gaussian Cluster-Weighted Model," Journal of Classification, Springer;The Classification Society, vol. 34(2), pages 249-293, July.
    5. Wang, Shaoli & Yao, Weixin & Huang, Mian, 2014. "A note on the identifiability of nonparametric and semiparametric mixtures of GLMs," Statistics & Probability Letters, Elsevier, vol. 93(C), pages 41-45.
    6. Angelo Mazza & Antonio Punzo, 2020. "Mixtures of multivariate contaminated normal regression models," Statistical Papers, Springer, vol. 61(2), pages 787-822, April.
    7. Sharon Lee & Geoffrey McLachlan, 2013. "Model-based clustering and classification with non-normal mixture distributions," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(4), pages 427-454, November.
    8. Tomarchio, Salvatore D. & Punzo, Antonio & Bagnato, Luca, 2020. "Two new matrix-variate distributions with application in model-based clustering," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    9. Alessio Farcomeni & Antonio Punzo, 2020. "Robust model-based clustering with mild and gross outliers," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(4), pages 989-1007, December.
    10. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    11. Francesca Greselin & Antonio Punzo, 2013. "Closed Likelihood Ratio Testing Procedures to Assess Similarity of Covariance Matrices," The American Statistician, Taylor & Francis Journals, vol. 67(3), pages 117-128, August.
    12. Francesca Greselin & Salvatore Ingrassia & Antonio Punzo, 2011. "Assessing the pattern of covariance matrices via an augmentation multiple testing procedure," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 20(2), pages 141-170, June.
    13. Biernacki, Christophe & Celeux, Gilles & Govaert, Gerard, 2003. "Choosing starting values for the EM algorithm for getting the highest likelihood in multivariate Gaussian mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 561-575, January.
    14. Kiers, Henk A. L., 2002. "Setting up alternating least squares and iterative majorization algorithms for solving various matrix optimization problems," Computational Statistics & Data Analysis, Elsevier, vol. 41(1), pages 157-170, November.
    15. Ryan Browne & Paul McNicholas, 2014. "Estimating common principal components in high dimensions," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 8(2), pages 217-226, June.
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