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

Abbas Mahdavi, Narayanaswamy Balakrishnan () and Ahad Jamalizadeh
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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

Mathematics, 2024, vol. 12, issue 20, 1-17

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.

Keywords: ECME algorithm; image segmentation; mixture models; matrix variate distributions; skewed distributions; truncated normal distribution; truncated t distribution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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