IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i20p3260-d1501036.html
   My bibliography  Save this article

Robust Classification via Finite Mixtures of Matrix Variate Skew- t Distributions

Author

Listed:
  • Abbas Mahdavi

    (Department of Statistics, Vali-e-Asr University of Rafsanjan, Rafsanjan 7718897111, Iran)

  • Narayanaswamy Balakrishnan

    (Department of Mathematics and Statistics, McMaster University, Hamilton, ON L8S 4K1, Canada)

  • Ahad Jamalizadeh

    (Department of Statistics, Faculty of Mathematics & Computer, Shahid Bahonar University of Kerman, Kerman 7616914111, Iran)

Abstract

Analysis of matrix variate data is becoming increasingly common in the literature, particularly in the field of clustering and classification. It is well known that real data, including real matrix variate data, often exhibit high levels of asymmetry. To address this issue, one common approach is to introduce a tail or skewness parameter to a symmetric distribution. In this regard, we introduce here a new distribution called the matrix variate skew- t distribution (MVST), which provides flexibility, in terms of heavy tail and skewness. We then conduct a thorough investigation of various characterizations and probabilistic properties of the MVST distribution. We also explore extensions of this distribution to a finite mixture model. To estimate the parameters of the MVST distribution, we develop an EM-type algorithm that computes maximum likelihood (ML) estimates of the model parameters. To validate the effectiveness and usefulness of the developed models and associated methods, we performed empirical experiments, using simulated data as well as three real data examples, including an application in skin cancer detection. Our results demonstrate the efficacy of the developed approach in handling asymmetric matrix variate data.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:20:p:3260-:d:1501036
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/20/3260/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/20/3260/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Rezaei, Amir & Yousefzadeh, Fatemeh & Arellano-Valle, Reinaldo B., 2020. "Scale and shape mixtures of matrix variate extended skew normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 179(C).
    2. 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).
    3. Tsung-I Lin & Pal Wu & Geoffrey McLachlan & Sharon Lee, 2015. "A robust factor analysis model using the restricted skew- $$t$$ t distribution," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 510-531, September.
    4. Sarkar, Shuchismita & Zhu, Xuwen & Melnykov, Volodymyr & Ingrassia, Salvatore, 2020. "On parsimonious models for modeling matrix data," Computational Statistics & Data Analysis, Elsevier, vol. 142(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    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. Stegeman, Alwin, 2016. "A new method for simultaneous estimation of the factor model parameters, factor scores, and unique parts," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 189-203.
    5. 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.
    6. 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).
    7. 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.
    8. Murray, Paula M. & Browne, Ryan P. & McNicholas, Paul D., 2017. "A mixture of SDB skew-t factor analyzers," Econometrics and Statistics, Elsevier, vol. 3(C), pages 160-168.
    9. Wan-Lun Wang & Min Liu & Tsung-I Lin, 2017. "Robust skew-t factor analysis models for handling missing data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(4), pages 649-672, November.
    10. 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.
    11. Sharon X. Lee & Tsung-I Lin & Geoffrey J. McLachlan, 2021. "Mixtures of factor analyzers with scale mixtures of fundamental skew 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. 15(2), pages 481-512, June.
    12. Abdullah Asilkalkan & Xuwen Zhu & Shuchismita Sarkar, 2024. "Finite mixture of hidden Markov models for tensor-variate time series 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. 18(3), pages 545-562, September.
    13. 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.
    14. 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.
    15. Tsung-I Lin & I-An Chen & Wan-Lun Wang, 2023. "A robust factor analysis model based on the canonical fundamental skew-t distribution," Statistical Papers, Springer, vol. 64(2), pages 367-393, April.
    16. 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.
    17. 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).
    18. Trang Quynh Nguyen & Elizabeth A. Stuart, 2020. "Propensity Score Analysis With Latent Covariates: Measurement Error Bias Correction Using the Covariate’s Posterior Mean, aka the Inclusive Factor Score," Journal of Educational and Behavioral Statistics, , vol. 45(5), pages 598-636, October.
    19. Hashemi, Farzane & Naderi, Mehrdad & Jamalizadeh, Ahad & Bekker, Andriette, 2021. "A flexible factor analysis based on the class of mean-mixture of normal distributions," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    20. Kim, Hea-Jung, 2018. "Bayesian hierarchical robust factor analysis models for partially observed sample-selection data," Journal of Multivariate Analysis, Elsevier, vol. 164(C), pages 65-82.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:12:y:2024:i:20:p:3260-:d:1501036. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.