41 citations · 264 across the 40 of their papers we have counts for
6 papers · 2 filters
Spatio-temporal Persistent Homology for Dynamic Metric Spaces
Woojin Kim, Facundo Memoli
Characterizing the dynamics of time-evolving data within the framework of topological data analysis (TDA) has been attracting increasingly more attention. Popular instances of time…
A Topological Study of Functional Data and Fréchet Functions of Metric Measure Spaces
Haibin Hang, Facundo Mémoli, Washington Mio
We study the persistent homology of both functional data on compact topological spaces and structural data presented as compact metric measure spaces. One of our goals is to define…
Generalized Persistence Diagrams for Persistence Modules over Posets
Woojin Kim, Facundo Memoli
When a category satisfies certain conditions, we define the notion of rank invariant for arbitrary poset-indexed functors from…
The reflection distance between zigzag persistence modules
Alexander Elchesen, Facundo Mémoli
By invoking the reflection functors introduced by Bernstein, Gelfand, and Ponomarev in 1973, in this paper we define a metric on the space of all zigzag modules of a given length,…
Quantitative Simplification of Filtered Simplicial Complexes
Facundo Mémoli, Osman Berat Okutan
We introduce a new invariant defined on the vertices of a given filtered simplicial complex, called codensity, which controls the impact of removing vertices on persistent homology…
The Reeb Graph Edit Distance is Universal
Ulrich Bauer, Claudia Landi, Facundo Memoli
We consider the setting of Reeb graphs of piecewise linear functions and study distances between them that are stable, meaning that functions which are similar in the supremum norm…