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arXiv · 2201.12933

Riemannian block SPD coupling manifold and its application to optimal transport

Andi Han·Bamdev Mishra·Pratik Jawanpuria·Junbin Gao
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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.

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BibTeXRIS

Andi Han, Bamdev Mishra, Pratik Jawanpuria, Junbin Gao. 2022-01-30. Riemannian block SPD coupling manifold and its application to optimal transport. https://arxiv.org/abs/2201.12933

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