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On parsimonious models for modeling matrix data

Author

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  • Sarkar, Shuchismita
  • Zhu, Xuwen
  • Melnykov, Volodymyr
  • Ingrassia, Salvatore

Abstract

Finite mixture modeling is a popular technique for capturing heterogeneity in data. Although the vast majority of the theory developed in this area up to date deals with vector-valued data, some recent advancements have been made to expand the concept to matrix-valued data, for example, by means of matrix Gaussian mixture models. Unfortunately, matrix mixtures tend to suffer from the overparameterization issue due to a high number of parameters involved in the model. As a result, this may lead to problems such as overfitting and mixture order underestimation. One possible approach of addressing the overparameterization issue that has proven to be effective in the vector-valued framework is to consider various parsimonious models. One of the most popular classes of parsimonious models is based on the spectral decomposition of covariance matrices. An attempt to generalize this class and make it applicable in the matrix setting is made. Estimation procedures are thoroughly discussed for all models considered. The application of the proposed methodology is studied on synthetic and real-life data sets.

Suggested Citation

  • Sarkar, Shuchismita & Zhu, Xuwen & Melnykov, Volodymyr & Ingrassia, Salvatore, 2020. "On parsimonious models for modeling matrix data," Computational Statistics & Data Analysis, Elsevier, vol. 142(C).
    • Handle: RePEc:eee:csdana:v:142:y:2020:i:c:s0167947319301690
    DOI: 10.1016/j.csda.2019.106822
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    Citations

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    Cited by:

    1. 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.
    2. Federico Ferraccioli & Giovanna Menardi, 2023. "Modal clustering of matrix-variate data," 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(2), pages 323-345, June.
    3. 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.
    4. Salvatore D. Tomarchio & Paul D. McNicholas & Antonio Punzo, 2021. "Matrix Normal Cluster-Weighted Models," Journal of Classification, Springer;The Classification Society, vol. 38(3), pages 556-575, October.
    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. Leonardo Salvatore Alaimo & Francesco Amato & Filomena Maggino & Alfonso Piscitelli & Emiliano Seri, 2023. "A Comparison of Migrant Integration Policies via Mixture of Matrix-Normals," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 165(2), pages 473-494, January.
    7. 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.
    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).

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