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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.
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On the approximation of the Riemannian barycenter
We present a method for computing an approximate Rieman-nian barycenter of a collection of points lying on a Riemannian mani-fold. Our approach relies on the use of theoretically proven under- and over-approximations of the Riemannian distance function. We compare it to Riemannian steepest descent on the exact objective function of the Riemannian barycenter and to an approach that approximates the Rie-mannian logarithm using lifting maps. Experiments are conducted on the Stiefel manifold.
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- Award ID(s):
- 2240158
- PAR ID:
- 10625575
- Publisher / Repository:
- 7th International Conference on Geometric Science of Information
- Date Published:
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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