A0343
Title: Barycenter estimation of positive semi-definite matrices with Bures-Wasserstein distance
Authors: Jingyi Zheng - Auburn University (United States) [presenting]
Huajun Huang - Auburn University (United States)
Yuyan Yi - Auburn University (United States)
Yuexin Li - Auburn University (United States)
Shu-Chin Lin - National Health Research Institutes (Taiwan)
Abstract: Brain-computer interface (BCI) builds a bridge between the human brain and external devices by recording brain signals and translating them into commands for devices to perform the user's imagined action. The core of the BCI system is the classifier that labels the input signals as the user's imagined action. The classifiers that directly classify covariance matrices using Riemannian geometry are widely used not only in the BCI domain but also in a variety of fields. However, the existing Affine-Invariant Riemannian-based methods suffer from issues such as being time-consuming, not robust, and having convergence issues when the dimension and number of covariance matrices become large. To address these challenges, the mathematical foundation is established for the Bures-Wasserstein distance and new algorithms are proposed to estimate the barycenter of positive semi-definite matrices efficiently and robustly. Both theoretical and computational aspects of Bures-Wasserstein distance and barycenter estimation algorithms are discussed. With extensive simulations, the accuracy, efficiency, and robustness of the barycenter estimation algorithms coupled with the Bures-Wasserstein distance are comprehensively investigated. The results show that Bures-Wasserstein-based barycenter estimation algorithms are more efficient and robust.
