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Two new matrix-variate distributions with application in model-based clustering

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  • Tomarchio, Salvatore D.
  • Punzo, Antonio
  • Bagnato, Luca

Abstract

Two matrix-variate distributions, both elliptical heavy-tailed generalization of the matrix-variate normal distribution, are introduced. They belong to the normal scale mixture family, and are respectively obtained by choosing a convenient shifted exponential or uniform as mixing distribution. Moreover, they have a closed-form for the probability density function that is characterized by only one additional parameter, with respect to the nested matrix-variate normal, governing the tail-weight. Both distributions are then used for model-based clustering via finite mixture models. The resulting mixtures, being able to handle data with atypical observations in a better way than the matrix-variate normal mixture, can avoid the disruption of the true underlying group structure. Different EM-based algorithms are implemented for parameter estimation and tested in terms of computational times and parameter recovery. Furthermore, these mixture models are fitted to simulated and real datasets, and their fitting and clustering performances are analyzed and compared to those obtained by other well-established competitors.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:csdana:v:152:y:2020:i:c:s0167947320301419
    DOI: 10.1016/j.csda.2020.107050
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    Cited by:

    1. 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.
    2. Žikica Lukić & Bojana Milošević, 2024. "A novel two-sample test within the space of symmetric positive definite matrix distributions and its application in finance," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 76(5), pages 797-820, October.
    3. 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.
    4. 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.
    5. Naderi, Mehrdad & Tamandi, Mostafa & Mirfarah, Elham & Wang, Wan-Lun & Lin, Tsung-I, 2024. "Three-way data clustering based on the mean-mixture of matrix-variate normal distributions," Computational Statistics & Data Analysis, Elsevier, vol. 199(C).
    6. 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.
    7. Abbas Mahdavi & Narayanaswamy Balakrishnan & Ahad Jamalizadeh, 2024. "Robust Classification via Finite Mixtures of Matrix Variate Skew- t Distributions," Mathematics, MDPI, vol. 12(20), pages 1-17, October.
    8. 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.

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