4 papers · 1 filter
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…
Equivalence of Landscape and Erosion Distances for Persistence Diagrams
Cagatay Ayhan, Tom Needham
This paper establishes connections between three of the most prominent metrics used in the analysis of persistence diagrams in topological data analysis: the bottleneck distance, P…
Metric properties of partial and robust Gromov-Wasserstein distances
Jannatul Chhoa, Michael Ivanitskiy, Fushuai Jiang +4
The Gromov-Wasserstein (GW) distances define a family of metrics, based on ideas from optimal transport, which enable comparisons between probability measures defined on distinct m…