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Article Dans Une Revue Algorithms Année : 2021

Subspace Detours Meet Gromov-Wasserstein

Résumé

In the context of optimal transport (OT) methods, the subspace detour approach was recently proposed by Muzellec and Cuturi. It consists of first finding an optimal plan between the measures projected on a wisely chosen subspace and then completing it in a nearly optimal transport plan on the whole space. The contribution of this paper is to extend this category of methods to the Gromov–Wasserstein problem, which is a particular type of OT distance involving the specific geometry of each distribution. After deriving the associated formalism and properties, we give an experimental illustration on a shape matching problem. We also discuss a specific cost for which we can show connections with the Knothe–Rosenblatt rearrangement.
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Dates et versions

hal-03500536 , version 1 (11-01-2024)

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Clément Bonet, Titouan Vayer, Nicolas Courty, François Septier, Lucas Drumetz. Subspace Detours Meet Gromov-Wasserstein. Algorithms, 2021, Special Issue Optimal Transport: Algorithms and Applications, 14 (12), pp.366. ⟨10.3390/a14120366⟩. ⟨hal-03500536⟩
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