Subspace Detours Meet Gromov-Wasserstein
Abstract
In the context of optimal transport methods, the subspace detour approach was recently presented by Muzellec and Cuturi (2019). It consists in building a nearly optimal transport plan in the measures space from an optimal transport plan in a wisely chosen subspace, onto which the original measures are projected. The contribution of this paper is to extend this category of methods to the Gromov-Wasserstein problem, which is a particular type of transport distance involving the inner geometry of the compared distributions. After deriving the associated formalism and properties, we also discuss a specific cost for which we can show connections with the Knothe-Rosenblatt rearrangement. We finally give an experimental illustration on a shape matching problem.
Cite
@article{arxiv.2110.10932,
title = {Subspace Detours Meet Gromov-Wasserstein},
author = {Clément Bonet and Nicolas Courty and François Septier and Lucas Drumetz},
journal= {arXiv preprint arXiv:2110.10932},
year = {2021}
}