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Riemannian block SPD coupling manifold and its application to optimal transport by Han, Andi; Mishra, Bamdev; Jawanpuria, Pratik; Gao, Junbin is a scholarly article available to read on EtoBox.

What is Riemannian block SPD coupling manifold and its application to optimal transport about?

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.

Author

Han, Andi; Mishra, Bamdev; Jawanpuria, Pratik; Gao, Junbin

Published

2022

Language

EN