20 citations · 40 across the 12 of their papers we have counts for
12 papers
Gromov-Hausdorff Distances Between Spheres: Asymptotics and Vietoris-Rips Coindex Bounds
Sunhyuk Lim, Facundo Mémoli, Qingsong Wang
For , let be the infimum of the scales at which the Vietoris-Rips simplicial complex of the unit round sphere , equipped with its geodesic met…
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…
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…
Reverse Bernstein Inequality on the Circle
Parvaneh Joharinad, Jürgen Jost, Sunhyuk Lim +1
The more then hundred years old Bernstein inequality states that the supremum norm of the derivative of a trigonometric polynomial of fixed degree can be bounded from above by supr…
The Weisfeiler-Lehman Distance: Reinterpretation and Connection with GNNs
Samantha Chen, Sunhyuk Lim, Facundo Mémoli +2
In this paper, we present a novel interpretation of the so-called Weisfeiler-Lehman (WL) distance, introduced by Chen et al. (2022), using concepts from stochastic processes. The W…
Gromov-Hausdorff distances, Borsuk-Ulam theorems, and Vietoris-Rips complexes
Henry Adams, Johnathan Bush, Nate Clause +13
We explore emerging relationships between the Gromov--Hausdorff distance, Borsuk--Ulam theorems, and Vietoris--Rips simplicial complexes. The Gromov--Hausdorff distance between two…
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…
Classical Multidimensional Scaling on Metric Measure Spaces
Sunhyuk Lim, Facundo Memoli
We generalize the classical Multidimensional Scaling procedure to the setting of general metric measure spaces. We develop a related spectral theory for the generalized cMDS operat…
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…
The Gromov-Hausdorff distance between spheres
Sunhyuk Lim, Facundo Mémoli, Zane Smith
We provide general upper and lower bounds for the Gromov-Hausdorff distance between spheres and (endowed…
Vietoris-Rips Persistent Homology, Injective Metric Spaces, and The Filling Radius
Sunhyuk Lim, Facundo Memoli, Osman Berat Okutan
In the applied algebraic topology community, the persistent homology induced by the Vietoris-Rips simplicial filtration is a standard method for capturing topological information f…