A0836
Title: Towards classification of covariance matrices via Bures-Wasserstein-based machine learning
Authors: Jingyi Zheng - Auburn University (United States) [presenting]
Yuyan Yi - Auburn University (United States)
Shu-Chin Lin - National Health Research Institutes (Taiwan)
Michael Zirpoli - Auburn University (United States)
Abstract: In the realm of machine learning, positive semi-definite (PSD) matrices emerge as crucial entities, especially in handling challenges posed by high-dimensional data. Three novel machine learning algorithms are introduced, tailored for the classification of PSD matrices on the manifold equipped with Bures-Wasserstein (BW) metric. Leveraging BW distance, barycenter estimation, and projection algorithms, the approach distinguishes itself from classical Euclidean methods by integrating the geometry of the Riemannian manifold where PSD matrices reside. In contrast to the prevalent Affine-Invariant (AI) Riemannian manifold analysis, the BW manifold analysis obviates the need for matrix regularization and significantly enhances computational efficiency. Additionally, a novel BW distance-based kernel function is proposed, which is further used in the kernel Support Vector Machine. Through comprehensive evaluations across multiple real datasets characterized by varying dimensions and matrix quantities, the findings underscore the exceptional performance of the proposed machine learning algorithms. The efficacy of BW metric-based machine learning methodologies in advancing the classification of PSD matrices is emphasized.
