Subspace Detours Meet Gromov–Wasserstein

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