Sunhyuk Lim
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View article: The G-Gromov-Hausdorff Distance and Equivariant Topology
The G-Gromov-Hausdorff Distance and Equivariant Topology Open
We made the following changes: (1) reorganized the section order, (2) added a subsection on the Gromov-Hausdorff distance between quotient spaces, and (3) added more examples and remarks.
View article: The Gromov–Wasserstein Distance Between Spheres
The Gromov–Wasserstein Distance Between Spheres Open
The Gromov–Wasserstein distance—a generalization of the usual Wasserstein distance—permits comparing probability measures defined on possibly different metric spaces. Recently, this notion of distance has found several applications in Data…
View article: Vietoris–Rips persistent homology, injectivemetric spaces, and the filling radius
Vietoris–Rips persistent homology, injectivemetric spaces, and the filling radius Open
In the applied algebraic topology community, the persistent homology induced by the Vietoris-Rips simplicial filtration is a standard method for capturing topological information from metric spaces. In this paper, we consider a different, …
View article: The Gromov–Hausdorff distance betweenspheres
The Gromov–Hausdorff distance betweenspheres Open
We provide general upper and lower bounds for the Gromov-Hausdorff distance $d_{\mathrm{GH}}(\mathbb{S}^m,\mathbb{S}^n)$ between spheres $\mathbb{S}^m$ and $\mathbb{S}^n$ (endowed with the round metric) for $0\leq m< n\leq \infty$. Some of…
View article: The Gromov-Wasserstein distance between spheres
The Gromov-Wasserstein distance between spheres Open
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 under…
Reverse Bernstein Inequality on the Circle Open
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 supremum norm of the polynomial itself. The reversed Bernstein …
View article: The Weisfeiler-Lehman Distance: Reinterpretation and Connection with GNNs
The Weisfeiler-Lehman Distance: Reinterpretation and Connection with GNNs Open
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 WL distance aims at comparing graphs with node features, has…
View article: Gromov-Hausdorff distances, Borsuk-Ulam theorems, and Vietoris-Rips complexes
Gromov-Hausdorff distances, Borsuk-Ulam theorems, and Vietoris-Rips complexes Open
We explore emerging relationships between the Gromov--Hausdorff distance, Borsuk--Ulam theorems, and Vietoris--Rips simplicial complexes. The Gromov--Hausdorff distance between two metric spaces $X$ and~$Y$ can be lower bounded by the dist…
Weisfeiler-Lehman meets Gromov-Wasserstein Open
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 graph neural networks. In this paper, we propose the Weisfeile…
Classical Multidimensional Scaling on Metric Measure Spaces Open
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 operator, which provides a more natural and rigorous mathematical…
Some results about the Tight Span of spheres Open
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 properties, and they are gradually becoming a target of research o…
The Gromov-Hausdorff distance between spheres Open
We provide general upper and lower bounds for the Gromov-Hausdorff distance $d_{\mathrm{GH}}(\mathbb{S}^m,\mathbb{S}^n)$ between spheres $\mathbb{S}^m$ and $\mathbb{S}^n$ (endowed with the round metric) for $0\leq m< n\leq \infty$. Some of…
Vietoris-Rips Persistent Homology, Injective Metric Spaces, and The Filling Radius Open
In the applied algebraic topology community, the persistent homology induced by the Vietoris-Rips simplicial filtration is a standard method for capturing topological information from metric spaces. In this paper, we consider a different, …