60 citations · 88 across the 15 of their papers we have counts for
16 papers
Random Walks, Conductance, and Resistance for the Connection Graph Laplacian
Alexander Cloninger, Gal Mishne, Andreas Oslandsbotn +3
We investigate the concept of effective resistance in connection graphs, expanding its traditional application from undirected graphs. We propose a robust definition of effective r…
A generalization of the persistent Laplacian to simplicial maps
Aziz Burak Gülen, Facundo Mémoli, Zhengchao Wan +1
The graph Laplacian is a fundamental object in the analysis of and optimization on graphs. This operator can be extended to a simplicial complex and therefore offers a way to p…
Distances for Markov Chains, and Their Differentiation
Tristan Brugère, Zhengchao Wan, Yusu Wang
(Directed) graphs with node attributes are a common type of data in various applications and there is a vast literature on developing metrics and efficient algorithms for comparing…
Understanding Oversquashing in GNNs through the Lens of Effective Resistance
Mitchell Black, Zhengchao Wan, Amir Nayyeri +1
Message passing graph neural networks (GNNs) are a popular learning architectures for graph-structured data. However, one problem GNNs experience is oversquashing, where a GNN has…
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…
The Numerical Stability of Hyperbolic Representation Learning
Gal Mishne, Zhengchao Wan, Yusu Wang +1
Given the exponential growth of the volume of the ball w.r.t. its radius, the hyperbolic space is capable of embedding trees with arbitrarily small distortion and hence has receive…
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…
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 ultrametric spaces: its structure and computation
Facundo Mémoli, Zane Smith, Zhengchao Wan
The Gromov-Hausdorff distance () provides a natural way of quantifying the dissimilarity between two given metric spaces. It is known that computing …
Characterization of Gromov-type geodesics
Facundo Mémoli, Zhengchao Wan
The collection of all isometry classes of compact metric spaces endowed with the Gromov-Hausdorff distance is known to be a geodesic space. However,…
The ultrametric Gromov-Wasserstein distance
Facundo Mémoli, Axel Munk, Zhengchao Wan +1
In this paper, we investigate compact ultrametric measure spaces which form a subset of the collection of all metric measure spaces . Similar as for…
Persistent Laplacians: properties, algorithms and implications
Facundo Mémoli, Zhengchao Wan, Yusu Wang
We present a thorough study of the theoretical properties and devise efficient algorithms for the \emph{persistent Laplacian}, an extension of the standard combinatorial Laplacian…
A novel construction of Urysohn universal ultrametric space via the Gromov-Hausdorff ultrametric
Zhengchao Wan
We establish universality and ultra-homogeneity of , the collection of all compact ultrametric spaces endowed with the so-called Gromov-Hausdorff ultra…
The Gaussian Transform
Kun Jin, Facundo Mémoli, Zhengchao Wan
We introduce the Gaussian transform (GT), an optimal transport inspired iterative method for denoising and enhancing latent structures in datasets. Under the hood, GT generates a n…
On -metric spaces and the -Gromov-Hausdorff distance
Facundo Mémoli, Zhengchao Wan
For each given we investigate certain sub-family of the collection of all compact metric spaces which are characterized by the satisf…
The Wasserstein transform
Kun Jin, Facundo Mémoli, Zane Smith +1
We introduce the Wasserstein Transform (WT), a general unsupervised framework for updating distance structures on given data sets with the purpose of enhancing features and denoisi…