41 citations · 264 across the 40 of their papers we have counts for
7 papers · 1 filter
The G-Gromov-Hausdorff Distance and Equivariant Topology
Sunhyuk Lim, Facundo Memoli
For each arbitrary finite group , we consider a suitable notion of Gromov Hausdorff distance between compact metric spaces and derive lower bounds based on equivariant topol…
The Gromov-Wasserstein distance between spheres
Shreya Arya, Arnab Auddy, Ranthony Edmonds +3
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 v…
Some results about the Tight Span of spheres
Sunhyuk Lim, Facundo Memoli, Zhengchao Wan +2
The smallest hyperconvex metric space containing a given metric space X is called the tight span of X. It is known that tight spans have many nice geometric and topological propert…
On the notion of weak isometry for finite metric spaces
Alessandro De Gregorio, Ulderico Fugacci, Facundo Memoli +1
Finite metric spaces are the object of study in many data analysis problems. We examine the concept of weak isometry between finite metric spaces, in order to analyse properties of…
Distance distributions and inverse problems for metric measure spaces
Facundo Mémoli, Tom Needham
Applications in data science, shape analysis and object classification frequently require comparison of probability distributions defined on different ambient spaces. To accomplish…
Metric Graph Approximations of Geodesic Spaces
Facundo Memoli, Osman Berat Okutan, Qingsong Wang
We study the question of approximating a compact geodesic metric space by metric graphs satisfying a uniform upper bound on their first Betti number. We prove that, up to a suitabl…