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Capturing patterns via parsimonious t mixture models

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  • Lin, Tsung-I
  • McNicholas, Paul D.
  • Ho, Hsiu J.

Abstract

Parsimonious mixtures of multivariate t-factor analyzers are used for robust clustering of high-dimensional data. Sixteen parsimonious mixtures of t-factor analyzers are utilized and the AECM algorithm is used for parameter estimation. Application to compact facial representation is illustrated.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:88:y:2014:i:c:p:80-87
    DOI: 10.1016/j.spl.2014.01.015
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    References listed on IDEAS

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    1. Wan-Lun Wang & Tsung-I Lin, 2013. "An efficient ECM algorithm for maximum likelihood estimation in mixtures of t-factor analyzers," Computational Statistics, Springer, vol. 28(2), pages 751-769, April.
    2. Andrews, Jeffrey L. & McNicholas, Paul D. & Subedi, Sanjeena, 2011. "Model-based classification via mixtures of multivariate t-distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 520-529, January.
    3. McLachlan, G. J. & Peel, D. & Bean, R. W., 2003. "Modelling high-dimensional data by mixtures of factor analyzers," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 379-388, January.
    4. McLachlan, G.J. & Bean, R.W. & Ben-Tovim Jones, L., 2007. "Extension of the mixture of factor analyzers model to incorporate the multivariate t-distribution," Computational Statistics & Data Analysis, Elsevier, vol. 51(11), pages 5327-5338, July.
    5. Tsung-I Lin & Hsiu Ho & Pao Shen, 2009. "Computationally efficient learning of multivariate t mixture models with missing information," Computational Statistics, Springer, vol. 24(3), pages 375-392, August.
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    Citations

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    Cited by:

    1. Michael P. B. Gallaugher & Salvatore D. Tomarchio & Paul D. McNicholas & Antonio Punzo, 2022. "Multivariate cluster weighted models using skewed 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. 16(1), pages 93-124, March.
    2. Cristina Tortora & Mireille Gettler Summa & Marina Marino & Francesco Palumbo, 2016. "Factor probabilistic distance clustering (FPDC): a new clustering method," 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. 10(4), pages 441-464, December.
    3. García-Escudero, Luis Angel & Gordaliza, Alfonso & Greselin, Francesca & Ingrassia, Salvatore & Mayo-Iscar, Agustín, 2016. "The joint role of trimming and constraints in robust estimation for mixtures of Gaussian factor analyzers," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 131-147.
    4. 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.
    5. Paula M. Murray & Ryan P. Browne & Paul D. McNicholas, 2020. "Mixtures of Hidden Truncation Hyperbolic Factor Analyzers," Journal of Classification, Springer;The Classification Society, vol. 37(2), pages 366-379, July.
    6. 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.
    7. Hosseini, Reshad & Sra, Suvrit & Theis, Lucas & Bethge, Matthias, 2016. "Inference and mixture modeling with the Elliptical Gamma Distribution," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 29-43.
    8. Ma, Xuan & Zhao, Jianhua & Wang, Yue & Shang, Changchun & Jiang, Fen, 2023. "Robust factored principal component analysis for matrix-valued outlier accommodation and detection," Computational Statistics & Data Analysis, Elsevier, vol. 179(C).
    9. Wan-Lun Wang & Tsung-I Lin, 2022. "Robust clustering via mixtures of t factor analyzers with incomplete 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. 16(3), pages 659-690, September.
    10. Wang, Wan-Lun & Lin, Tsung-I, 2016. "Maximum likelihood inference for the multivariate t mixture model," Journal of Multivariate Analysis, Elsevier, vol. 149(C), pages 54-64.
    11. Wei, Yuhong & Tang, Yang & McNicholas, Paul D., 2019. "Mixtures of generalized hyperbolic distributions and mixtures of skew-t distributions for model-based clustering with incomplete data," Computational Statistics & Data Analysis, Elsevier, vol. 130(C), pages 18-41.
    12. Reyhaneh Rikhtehgaran & Iraj Kazemi, 2016. "The determination of uncertainty levels in robust clustering of subjects with longitudinal observations using the Dirichlet process mixture," 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. 10(4), pages 541-562, December.
    13. Paul D. McNicholas, 2016. "Model-Based Clustering," Journal of Classification, Springer;The Classification Society, vol. 33(3), pages 331-373, October.
    14. Kim, Nam-Hwui & Browne, Ryan P., 2021. "In the pursuit of sparseness: A new rank-preserving penalty for a finite mixture of factor analyzers," Computational Statistics & Data Analysis, Elsevier, vol. 160(C).
    15. Cristina Tortora & Paul D. McNicholas & Ryan P. Browne, 2016. "A mixture of generalized hyperbolic 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. 10(4), pages 423-440, December.
    16. Michael P. B. Gallaugher & Paul D. McNicholas, 2019. "On Fractionally-Supervised Classification: Weight Selection and Extension to the Multivariate t-Distribution," Journal of Classification, Springer;The Classification Society, vol. 36(2), pages 232-265, July.
    17. Utkarsh J. Dang & Antonio Punzo & Paul D. McNicholas & Salvatore Ingrassia & Ryan P. Browne, 2017. "Multivariate Response and Parsimony for Gaussian Cluster-Weighted Models," Journal of Classification, Springer;The Classification Society, vol. 34(1), pages 4-34, April.
    18. 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.
    19. Morris, Katherine & McNicholas, Paul D., 2016. "Clustering, classification, discriminant analysis, and dimension reduction via generalized hyperbolic mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 97(C), pages 133-150.

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