Timezone: »
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.
Author Information
Clément Bonet (Université de Bretagne Sud)
Nicolas Courty (IRISA / University South Brittany)
François Septier
Lucas Drumetz (IMT Atlantique)
Related Events (a corresponding poster, oral, or spotlight)
-
2021 : Subspace Detours Meet Gromov-Wasserstein »
Dates n/a. Room
More from the Same Authors
-
2021 : Factored couplings in multi-marginal optimal transport via difference of convex programming »
Quang Huy TRAN · Hicham Janati · Ievgen Redko · Rémi Flamary · Nicolas Courty -
2021 : Factored couplings in multi-marginal optimal transport via difference of convex programming »
Quang Huy TRAN · Hicham Janati · Ievgen Redko · Rémi Flamary · Nicolas Courty -
2022 : Turning Normalizing Flows into Monge Maps with Geodesic Gaussian Preserving Flows »
Guillaume Morel · Lucas Drumetz · Nicolas Courty · François Rousseau · Simon Benaïchouche -
2017 Poster: Joint distribution optimal transportation for domain adaptation »
Nicolas Courty · Rémi Flamary · Amaury Habrard · Alain Rakotomamonjy -
2016 Poster: Optimal spectral transportation with application to music transcription »
Rémi Flamary · Cédric Févotte · Nicolas Courty · Valentin Emiya -
2016 Poster: Mapping Estimation for Discrete Optimal Transport »
Michaël Perrot · Nicolas Courty · Rémi Flamary · Amaury Habrard