Symmetric Positive Semi-definite Riemannian Geometry with Application to Domain Adaptation

2020/07/28 by Or Yair, Yair, Or, Almog Lahav +3
Computer Science · Engineering · #Advanced Vision and Imaging #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Medical Image Segmentation Techniques #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.2007.14272

openalex publication_date 2020/07/28 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

In this paper, we present new results on the Riemannian geometry of symmetric positive semi-definite (SPSD) matrices. First, based on an existing approximation of the geodesic path, we introduce approximations of the logarithmic and exponential maps. Second, we present a closed-form expression for Parallel Transport (PT). Third, we derive a canonical representation for a set of SPSD matrices. Based on these results, we propose an algorithm for Domain Adaptation (DA) and demonstrate its performance in two applications: fusion of hyper-spectral images and motion identification.

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• Riemannian block SPD coupling manifold and its application to optimal transport