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Conference Papers Year : 2021

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.
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Dates and versions

hal-03426813 , version 1 (12-07-2024)

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Clément Bonet, Nicolas Courty, François Septier, Lucas Drumetz. Subspace Detours Meet Gromov-Wasserstein. NeurIPS, workshop on Optimal Transport in Machine Learning, Dec 2021, Virtual-only Conference, France. ⟨10.48550/arXiv.2110.10932⟩. ⟨hal-03426813⟩
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