Facundo Mémoli

research

∙ 03/14/2023

Meta-Diagrams for 2-Parameter Persistence

We first introduce the notion of meta-rank for a 2-parameter persistence...

0 Nate Clause, et al. ∙

research

∙ 02/07/2023

A generalization of the persistent Laplacian to simplicial maps

The graph Laplacian is a fundamental object in the analysis of and optim...

0 Aziz Burak Gülen, et al. ∙

research

∙ 02/01/2023

The Weisfeiler-Lehman Distance: Reinterpretation and Connection with GNNs

In this paper, we present a novel interpretation of the so-called Weisfe...

0 Samantha Chen, et al. ∙

research

∙ 07/23/2022

The discriminating power of the generalized rank invariant

The rank invariant (RI), one of the best known invariants of persistence...

0 Nate Clause, et al. ∙

research

∙ 02/05/2022

Weisfeiler-Lehman meets Gromov-Wasserstein

The Weisfeiler-Lehman (WL) test is a classical procedure for graph isomo...

0 Samantha Chen, et al. ∙

research

∙ 11/30/2021

Computing Generalized Rank Invariant for 2-Parameter Persistence Modules via Zigzag Persistence and its Applications

The notion of generalized rank invariant in the context of multiparamete...

0 Tamal K. Dey, et al. ∙

research

∙ 10/07/2021

The Gromov-Hausdorff distance between ultrametric spaces: its structure and computation

The Gromov-Hausdorff distance (d_GH) provides a natural way of quantifyi...

0 Facundo Mémoli, et al. ∙

research

∙ 08/16/2021

Robust Hierarchical Clustering for Directed Networks: An Axiomatic Approach

We provide a complete taxonomic characterization of robust hierarchical ...

2 Gunnar Carlsson, et al. ∙

research

∙ 07/04/2021

Persistent Cup-Length

Cohomological ideas have recently been injected into persistent homology...

0 Marco Contessoto, et al. ∙

research

∙ 12/04/2020

Persistent Laplacians: properties, algorithms and implications

The combinatorial graph Laplacian has been a fundamental object in the a...

0 Facundo Mémoli, et al. ∙

research

∙ 06/21/2020

The Gaussian Transform

We introduce the Gaussian transform (GT), an optimal transport inspired ...

0 Kun Jin, et al. ∙

research

∙ 03/10/2020

Elder-Rule-Staircodes for Augmented Metric Spaces

An augmented metric space is a metric space (X, d_X) equipped with a fun...

0 Chen Cai, et al. ∙

research

∙ 01/21/2020

Vietoris-Rips Persistent Homology, Injective Metric Spaces, and The Filling Radius

In the applied algebraic topology community, the persistent homology ind...

0 Sunhyuk Lim, et al. ∙

research

∙ 01/01/2020

Motivic clustering schemes for directed graphs

Motivated by the concept of network motifs we construct certain clusteri...

1 Guilherme Vituri F. Pinto, et al. ∙

research

∙ 12/28/2019

Persistent Homotopy Groups of Metric Spaces

We study notions of persistent homotopy groups of compact metric spaces ...

0 Facundo Mémoli, et al. ∙

research

∙ 10/21/2019

Sampling random graph homomorphisms and applications to network data analysis

A graph homomorphism is a map between two graphs that preserves adjacenc...

25 Hanbaek Lyu, et al. ∙

research

∙ 05/31/2019

A Primer on Persistent Homology of Finite Metric Spaces

TDA (topological data analysis) is a relatively new area of research rel...

0 Facundo Mémoli, et al. ∙

research

∙ 12/03/2018

Stable Persistent Homology Features of Dynamic Metric Spaces

Characterizing the dynamics of time-evolving data within the framework o...

0 Woojin Kim, et al. ∙

research

∙ 10/26/2018

Generalized Persistence Diagrams for Persistence Modules over Posets

When a category C satisfies certain conditions, we define the notion of ...

0 Woojin Kim, et al. ∙

research

∙ 10/26/2018

Rank invariant for Zigzag Modules

The rank invariant is of great interest in studying both one-dimensional...

0 Woojin Kim, et al. ∙

research

∙ 10/17/2018

The Wasserstein transform

We introduce the Wasserstein transform, a method for enhancing and denoi...

0 Facundo Mémoli, et al. ∙

research

∙ 08/13/2018

The Gromov-Wasserstein distance between networks and stable network invariants

We define a metric---the Network Gromov-Wasserstein distance---on weight...

0 Samir Chowdhury, et al. ∙

research

∙ 05/28/2018

The reflection distance between zigzag persistence modules

By invoking the reflection functors introduced by Bernstein, Gelfand, an...

0 Alexander Elchesen, et al. ∙

research

∙ 04/09/2018

The Metric Space of Networks

We study the question of reconstructing a weighted, directed network up ...

0 Samir Chowdhury, et al. ∙

research

∙ 01/05/2018

The Reeb Graph Edit Distance is Universal

We consider the setting of Reeb graphs of piecewise linear functions and...

0 Ulrich Bauer, et al. ∙

research

∙ 01/02/2018

Sketching and Clustering Metric Measure Spaces

Two important optimization problems in the analysis of geometric data se...

0 Facundo Mémoli, et al. ∙

research

∙ 12/11/2017

Stable Signatures for Dynamic Graphs and Dynamic Metric Spaces via Zigzag Persistence

When studying flocking/swarming behaviors in animals one is interested i...

0 Woojin Kim, et al. ∙

research

∙ 12/11/2017

Stable Signatures for Dynamic Metric Spaces via Zigzag Persistent Homology

When studying flocking/swarming behaviors in animals one is interested i...

0 Woojin Kim, et al. ∙

research

∙ 11/12/2017

Convergence of Hierarchical Clustering and Persistent Homology Methods on Directed Networks

While there has been much interest in adapting conventional clustering p...

0 Samir Chowdhury, et al. ∙

research

∙ 08/16/2017

Distances and Isomorphism between Networks and the Stability of Network Invariants

We develop the theoretical foundations of a network distance that has re...

0 Samir Chowdhury, et al. ∙

research

∙ 07/21/2016

Admissible Hierarchical Clustering Methods and Algorithms for Asymmetric Networks

This paper characterizes hierarchical clustering methods that abide by t...

0 Gunnar Carlsson, et al. ∙

research

∙ 07/21/2016

Hierarchical Clustering of Asymmetric Networks

This paper considers networks where relationships between nodes are repr...

1 Gunnar Carlsson, et al. ∙

research

∙ 09/15/2015

The Shape of Data and Probability Measures

We introduce the notion of multiscale covariance tensor fields (CTF) ass...

0 Diego Hernán Díaz Martínez, et al. ∙

research

∙ 04/17/2014

Hierarchical Quasi-Clustering Methods for Asymmetric Networks

This paper introduces hierarchical quasi-clustering methods, a generaliz...

0 Gunnar Carlsson, et al. ∙

research

∙ 01/31/2013

Axiomatic Construction of Hierarchical Clustering in Asymmetric Networks

This paper considers networks where relationships between nodes are repr...

0 Gunnar Carlsson, et al. ∙

research

∙ 11/24/2010

Classifying Clustering Schemes

Many clustering schemes are defined by optimizing an objective function ...

0 Gunnar Carlsson, et al. ∙

research

∙ 08/16/2008

Persistent Clustering and a Theorem of J. Kleinberg

We construct a framework for studying clustering algorithms, which inclu...

0 Gunnar Carlsson, et al. ∙

Facundo Mémoli

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