Symmetric Positive Semi-definite Riemannian Geometry with Application to
Domain Adaptation
- URL: http://arxiv.org/abs/2007.14272v2
- Date: Tue, 4 Aug 2020 16:00:03 GMT
- Title: Symmetric Positive Semi-definite Riemannian Geometry with Application to
Domain Adaptation
- Authors: Or Yair, Almog Lahav, and Ronen Talmon
- Abstract summary: We present new results on the geometry of symmetric positive semi-definite (SPSD) matrices.
We propose an algorithm for Domain Adaptation (DA) and demonstrate its performance in two applications: fusion of hyper-spectral images and motion identification.
- Score: 7.126737403006778
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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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