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Riemannian block SPD coupling manifold and its application to optimal transport.
- Source :
- Machine Learning; Apr2024, Vol. 113 Issue 4, p1595-1622, 28p
- Publication Year :
- 2024
-
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. [ABSTRACT FROM AUTHOR]
- Subjects :
- CENTROID
Subjects
Details
- Language :
- English
- ISSN :
- 08856125
- Volume :
- 113
- Issue :
- 4
- Database :
- Complementary Index
- Journal :
- Machine Learning
- Publication Type :
- Academic Journal
- Accession number :
- 176338110
- Full Text :
- https://doi.org/10.1007/s10994-022-06258-w