mlsanityData to 14 Oct 2026

Subspace Detours Meet Gromov-Wasserstein

arXiv 2110.10932 ↗First posted 21 Oct 2021cs.LG math.OC stat.MLcited by 4

Not on the map. Why?

Abstract (arXiv)

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.

Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Builds on 16 of its 47 references that are in the map. First posted on arXiv 21 Oct 2021.

Builds on

16 of 47 references.

References · 16

  1. 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,316
  2. 2015Optimal Transport for Domain Adaptationcited by 463
  3. 2018Optimal Transport for structured data with application on graphscited by 172
  4. 2019Scalable Gromov-Wasserstein Learning for Graph Partitioning and Matchingcited by 103
  5. 2019Subspace Robust Wasserstein Distancescited by 90
  6. 2019Sliced Gromov-Wassersteincited by 66
  7. 2021Minibatch optimal transport distances; analysis and applicationscited by 65
  8. 2016Convergence Rate of Frank-Wolfe for Non-Convex Objectivescited by 63
  9. 2019Sum-of-Squares Polynomial Flowcited by 62
  10. 2021Linear-Time Gromov Wasserstein Distances using Low Rank Couplings and Costscited by 61
  11. 2020Generalized Spectral Clustering via Gromov-Wasserstein Learningcited by 38
  12. 2020On Projection Robust Optimal Transport: Sample Complexity and Model Misspecificationcited by 34
4 more
  1. 2018Towards Optimal Transport with Global Invariancescited by 33
  2. 2019Subspace Detours: Building Transport Plans that are Optimal on Subspace Projectionscited by 19
  3. 2021Quantized Gromov-Wassersteincited by 19
  4. 2020A contribution to Optimal Transport on incomparable spacescited by 15

Built on by

Cited by year

Citing papers per year: 2022: 1; 2023: 3.

4 papers.

  1. 2022Meta Optimal Transportcited by 28
  2. 2023Scalable Optimal Transport Methods in Machine Learning: A Contemporary Surveycited by 27
  3. 2023Learning representations that are closed-form Monge mapping optimal with application to domain adaptationcited by 2
  4. 2023Interpolating between Clustering and Dimensionality Reduction with Gromov-Wassersteincited by 0