41 citations · 264 across the 40 of their papers we have counts for
13 papers · 1 filter
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…
Distance distributions and inverse problems for metric measure spaces
Facundo Mémoli, Tom Needham
Applications in data science, shape analysis and object classification frequently require comparison of probability distributions defined on different ambient spaces. To accomplish…
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…
Metric Graph Approximations of Geodesic Spaces
Facundo Memoli, Osman Berat Okutan, Qingsong Wang
We study the question of approximating a compact geodesic metric space by metric graphs satisfying a uniform upper bound on their first Betti number. We prove that, up to a suitabl…