Subspace Detours Meet Gromov-Wasserstein
- URL: http://arxiv.org/abs/2110.10932v1
- Date: Thu, 21 Oct 2021 07:04:28 GMT
- Title: Subspace Detours Meet Gromov-Wasserstein
- Authors: Cl\'ement Bonet, Nicolas Courty, Fran\c{c}ois Septier, Lucas Drumetz
- Abstract summary: The subspace detour approach was recently presented by Muzellec and Cuturi.
The contribution of this paper is to extend this category of methods to the Gromov-Wasserstein problem.
- Score: 15.048733056992855
- License: http://creativecommons.org/licenses/by/4.0/
- 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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