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- Title
Riemannian block SPD coupling manifold and its application to optimal transport.
- Authors
Han, Andi; Mishra, Bamdev; Jawanpuria, Pratik; Gao, Junbin
- Abstract
In this work, we study the optimal transport (OT) problem between symmetric positive definite (SPD) matrix-valued measures. We formulate the above as a generalized optimal transport problem where the cost, the marginals, and the coupling are represented as block matrices and each component block is a SPD matrix. The summation of row blocks and column blocks in the coupling matrix are constrained by the given block-SPD marginals. We endow the set of such block-coupling matrices with a novel Riemannian manifold structure. This allows to exploit the versatile Riemannian optimization framework to solve generic SPD matrix-valued OT problems. We illustrate the usefulness of the proposed approach in several applications.
- Subjects
CENTROID
- Publication
Machine Learning, 2024, Vol 113, Issue 4, p1595
- ISSN
0885-6125
- Publication type
Article
- DOI
10.1007/s10994-022-06258-w