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Mixtures of skewed matrix variate bilinear factor analyzers

Author

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  • Michael P. B. Gallaugher

    (McMaster University)

  • Paul D. McNicholas

    (McMaster University)

Abstract

In recent years, data have become increasingly higher dimensional and, therefore, an increased need has arisen for dimension reduction techniques for clustering. Although such techniques are firmly established in the literature for multivariate data, there is a relative paucity in the area of matrix variate, or three-way, data. Furthermore, the few methods that are available all assume matrix variate normality, which is not always sensible if cluster skewness or excess kurtosis is present. Mixtures of bilinear factor analyzers using skewed matrix variate distributions are proposed. In all, four such mixture models are presented, based on matrix variate skew-t, generalized hyperbolic, variance-gamma, and normal inverse Gaussian distributions, respectively.

Suggested Citation

  • Michael P. B. Gallaugher & Paul D. McNicholas, 2020. "Mixtures of skewed matrix variate bilinear factor analyzers," 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. 14(2), pages 415-434, June.
    • Handle: RePEc:spr:advdac:v:14:y:2020:i:2:d:10.1007_s11634-019-00377-4
    DOI: 10.1007/s11634-019-00377-4
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    References listed on IDEAS

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    1. Vrbik, I. & McNicholas, P.D., 2012. "Analytic calculations for the EM algorithm for multivariate skew-t mixture models," Statistics & Probability Letters, Elsevier, vol. 82(6), pages 1169-1174.
    2. Murray, Paula M. & Browne, Ryan P. & McNicholas, Paul D., 2017. "Hidden truncation hyperbolic distributions, finite mixtures thereof, and their application for clustering," Journal of Multivariate Analysis, Elsevier, vol. 161(C), pages 141-156.
    3. Gallaugher, Michael P.B. & McNicholas, Paul D., 2019. "Three skewed matrix variate distributions," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 103-109.
    4. Utkarsh J. Dang & Ryan P. Browne & Paul D. McNicholas, 2015. "Mixtures of multivariate power exponential distributions," Biometrics, The International Biometric Society, vol. 71(4), pages 1081-1089, December.
    5. Morris, Katherine & McNicholas, Paul D., 2013. "Dimension reduction for model-based clustering via mixtures of shifted asymmetric Laplace distributions," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 2088-2093.
    6. Xiao‐Li Meng & David Van Dyk, 1997. "The EM Algorithm—an Old Folk‐song Sung to a Fast New Tune," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(3), pages 511-567.
    7. Cristina Tortora & Brian C. Franczak & Ryan P. Browne & Paul D. McNicholas, 2019. "A Mixture of Coalesced Generalized Hyperbolic Distributions," Journal of Classification, Springer;The Classification Society, vol. 36(1), pages 26-57, April.
    8. Lin, Tsung-I & McNicholas, Paul D. & Ho, Hsiu J., 2014. "Capturing patterns via parsimonious t mixture models," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 80-87.
    9. Melnykov, Volodymyr & Zhu, Xuwen, 2018. "On model-based clustering of skewed matrix data," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 181-194.
    10. Vrbik, Irene & McNicholas, Paul D., 2014. "Parsimonious skew mixture models for model-based clustering and classification," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 196-210.
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