Correlated Wishart matrices classification via an expectation-maximization composite likelihood-based algorithm

Positive-definite matrix-variate data is becoming popular in computer vision. The computer vision data descriptors in the form of Region Covariance Descriptors (RCD) are positive definite matrices, which extract the key features of the images. The RCDs are extensively used in image set classification. Some classification methods treating RCDs as Wishart distributed random matrices are being proposed. However, the majority of the current methods preclude the potential correlation among the RCDs caused by the so-called auxiliary information (e.g., subjects’ ages and nose widths, etc). Modeling correlated Wishart matrices is difficult since the joint density function of correlated Wishart matrices is difficult to be obtained. In this paper, we propose an Expectation-Maximization composite likelihoodbased algorithm of Wishart matrices to tackle this issue. Given the numerical studies based on the synthetic data and the real data (Chicago face data-set), our proposed algorithm performs better than the alternative methods which do not consider the correlation caused by the so-called auxiliary information.

Keywords

correlated Wishart matrices, composite likelihood, computer vision, expectation–-maximization algorithm, image set classification, region covariance descriptor

2010 Mathematics Subject Classification

Primary 62H10. Secondary 62H30.

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Received 17 August 2021

Accepted 5 December 2022

Published 1 February 2024