5 papers
Vietoris--Rips Coindex Thresholds for Round Spheres: Spherical Joins and Chromatic Obstructions for Gromov--Hausdorff Distances
Sunhyuk Lim, Facundo Mémoli, Qingsong Wang
For , let be the infimum of scales at which the Vietoris--Rips filtration of the round sphere admits a continuous odd map from .…
The Gromov-Hausdorff Distance Between Consecutive Spheres
Donghan Kim, Sunhyuk Lim, Facundo Memoli
We determine the Gromov-Hausdorff distance between consecutive unit round spheres equipped with their geodesic metrics. Put the common geodesic dis…
Metric Geometry of Lebesgue, Wasserstein, and Gromov-Wasserstein Spaces: Submetries, Curvature, and Geodesics
Martin Bauer, Facundo Mémoli, Tom Needham +1
A metric space gives rise to three natural classes of infinite-dimensional metric spaces associated to : -Wasserstein spaces of probability measures on , nonlinear Leb…
The Z-Gromov-Wasserstein Distance
Martin Bauer, Facundo Mémoli, Tom Needham +1
The Gromov-Wasserstein (GW) distance is a powerful tool for comparing metric measure spaces which has found broad applications in data science and machine learning. Driven by the n…
Weisfeiler-Lehman meets Gromov-Wasserstein
Samantha Chen, Sunhyuk Lim, Facundo Mémoli +2
The Weisfeiler-Lehman (WL) test is a classical procedure for graph isomorphism testing. The WL test has also been widely used both for designing graph kernels and for analyzing gra…