Symmetric Positive Semi-definite Riemannian Geometry with Application to Domain Adaptation
This work provides incremental improvements in geometric methods for domain adaptation, potentially benefiting fields like computer vision and signal processing.
The paper tackled the problem of developing Riemannian geometry tools for symmetric positive semi-definite matrices and applied them to domain adaptation, demonstrating performance in hyper-spectral image fusion and motion identification.
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.