Towards Analysis of Covariance Descriptors via Bures–Wasserstein Distance

Huajun Huang, Yuexin Li, Shu-Chin Lin, Yuyan Yi and Jingyi Zheng ()
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Huajun Huang: Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849, USA
Yuexin Li: Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849, USA
Shu-Chin Lin: Institute of Statistics and Data Science, National Taiwan University, Taipei 106319, Taiwan
Yuyan Yi: Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849, USA
Jingyi Zheng: Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849, USA

Mathematics, 2025, vol. 13, issue 13, 1-26

Abstract: A brain–computer interface (BCI) provides a direct communication pathway between the human brain and external devices, enabling users to control them through thought. It records brain signals and classifies them into specific commands for external devices. Among various classifiers used in BCI, those directly classifying covariance matrices using Riemannian geometry find broad applications not only in BCI, but also in diverse fields such as computer vision, natural language processing, domain adaption, and remote sensing. However, the existing Riemannian-based methods exhibit limitations, including time-intensive computations, susceptibility to disturbances, and convergence challenges in scenarios involving high-dimensional matrices. In this paper, we tackle these issues by introducing the Bures–Wasserstein (BW) distance for covariance matrices analysis and demonstrating its advantages in BCI applications. Both theoretical and computational aspects of BW distance are investigated, along with algorithms for Fréchet Mean (or barycenter) estimation using BW distance. Extensive simulations are conducted to evaluate the effectiveness, efficiency, and robustness of the BW distance and barycenter. Additionally, by integrating BW barycenter into the Minimum Distance to Riemannian Mean classifier, we showcase its superior classification performance through evaluations on five real datasets.

Keywords: brain–computer interface (BCI); Riemannian manifold; affine-invariant distance; Bures–Wasserstein distance; Fréchet Mean; barycenter (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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