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On model-based clustering of skewed matrix data

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  • Melnykov, Volodymyr
  • Zhu, Xuwen

Abstract

The existing finite mixture modeling and model-based clustering literature focuses primarily on the analysis of multivariate data observed in the form of vectors, with each element representing a specific feature. In this setting, multivariate Gaussian mixture models have been the most commonly used. Due to severe modeling issues observed when normal components cannot provide adequate fit to groups, much attention has been paid to developing models capable of accounting for skewness in data. In our work, we target the problem of mixture modeling with components that can handle skewness in matrix-valued data. The proposed developments open a wide range of possible modeling capabilities, with numerous applications, as illustrated in this paper. A novel matrix mixture model is proposed. Its skewness parameters enjoy appealing interpretability. The corresponding estimation procedure and various ways of parameterization are discussed. Comprehensive simulation studies and applications to real-life datasets illustrate the efficiency of the proposed developments, supported by good results.

Suggested Citation

  • Melnykov, Volodymyr & Zhu, Xuwen, 2018. "On model-based clustering of skewed matrix data," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 181-194.
    • Handle: RePEc:eee:jmvana:v:167:y:2018:i:c:p:181-194
    DOI: 10.1016/j.jmva.2018.04.007
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    References listed on IDEAS

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    Cited by:

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    3. Xuwen Zhu & Yana Melnykov, 2022. "On Finite Mixture Modeling of Change-point Processes," Journal of Classification, Springer;The Classification Society, vol. 39(1), pages 3-22, March.
    4. Sanjeena Subedi & Paul D. McNicholas, 2021. "A Variational Approximations-DIC Rubric for Parameter Estimation and Mixture Model Selection Within a Family Setting," Journal of Classification, Springer;The Classification Society, vol. 38(1), pages 89-108, April.
    5. Xuwen Zhu & Shuchismita Sarkar & Volodymyr Melnykov, 2022. "MatTransMix: an R Package for Matrix Model-Based Clustering and Parsimonious Mixture Modeling," Journal of Classification, Springer;The Classification Society, vol. 39(1), pages 147-170, March.
    6. Alex Sharp & Glen Chalatov & Ryan P. Browne, 2023. "A dual subspace parsimonious mixture of matrix normal distributions," 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. 17(3), pages 801-822, September.
    7. Sharon M. McNicholas & Paul D. McNicholas & Daniel A. Ashlock, 2021. "An Evolutionary Algorithm with Crossover and Mutation for Model-Based Clustering," Journal of Classification, Springer;The Classification Society, vol. 38(2), pages 264-279, July.
    8. Punzo, Antonio & Bagnato, Luca, 2022. "Dimension-wise scaled normal mixtures with application to finance and biometry," Journal of Multivariate Analysis, Elsevier, vol. 191(C).
    9. Punzo, Antonio & Bagnato, Luca, 2021. "Modeling the cryptocurrency return distribution via Laplace scale mixtures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 563(C).
    10. Donatella Vicari & Paolo Giordani, 2023. "CPclus: Candecomp/Parafac Clustering Model for Three-Way Data," Journal of Classification, Springer;The Classification Society, vol. 40(2), pages 432-465, July.
    11. Kozubowski, Tomasz J. & Mazur, Stepan & Podgorski, Krysztof, 2022. "Matrix Variate Generalized Laplace Distributions," Working Papers 2022:7, Örebro University, School of Business.

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