The Gromov-Wasserstein distance between spheres
Metric Geometry
2024-07-15 v3 Optimization and Control
Abstract
In this paper we consider a two-parameter family {dGWp,q}p,q of Gromov- Wasserstein distances between metric measure spaces. By exploiting a suitable interaction between specific values of the parameters p and q and the metric of the underlying spaces, we determine the exact value of the distance dGW4,2 between all pairs of unit spheres of different dimension endowed with their Euclidean distance and their uniform measure.
Keywords
Cite
@article{arxiv.2306.10586,
title = {The Gromov-Wasserstein distance between spheres},
author = {Shreya Arya and Arnab Auddy and Ranthony Edmonds and Sunhyuk Lim and Facundo Memoli and Daniel Packer},
journal= {arXiv preprint arXiv:2306.10586},
year = {2024}
}
Comments
1. Added a Section 4, Section 5, and Appendix C; 2. Swapped Sections 2 and 3; 3. "Relagated Proofs" section (Section 4 in the old version) is now in appendix