Geometric Characteristics of the Wasserstein Metric on SPD(n) and Its Applications on Data Processing

• Published in: Entropy (Basel, Switzerland) Vol. 23; no. 9; p. 1214
• Main Authors: Luo, Yihao, Zhang, Shiqiang, Cao, Yueqi, Sun, Huafei
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 14.09.2021; MDPI
• Subjects: Algorithms; Artificial intelligence; Curvature; Data processing; Decomposition; Eigenvalues; Geodesy; Geometry; image edge detecting; Mathematical analysis; Matrices (mathematics); point cloud denoising; symmetric positive-definite matrix; Symmetry; Wasserstein metric

The Wasserstein distance, especially among symmetric positive-definite matrices, has broad and deep influences on the development of artificial intelligence (AI) and other branches of computer science. In this paper, by involving the Wasserstein metric on SPD(n), we obtain computationally feasible e...