3 citations · 5 across the 10 of their papers we have counts for
12 papers
Persistent Homology and Equivariance in Data Analysis: A Topological Introduction
Patrizio Frosini, Ulderico Fugacci, Nicola Quercioli +1
This new book is intended as a first elementary introduction to Topological Data Analysis for mathematics students seeking a rigorous account of the foundations of persistent homol…
Stratified Morse Theory for Cell Complexes
Vidit Nanda, Francesca Tombari
We develop a version of discrete Morse theory for finite regular CW complexes equipped with an auxiliary stratification. The key construction is the halo of a cell, which contains…
The Convex Matching Distance in Multiparameter Persistence
Francesco Conti, Patrizio Frosini, Ulderico Fugacci +4
We introduce the convex matching distance, a novel metric for comparing functions with values in the real plane. This metric measures the maximal bottleneck distance between the pe…
Gromov-Hausdorff Distance for Directed Spaces
Lisbeth Fajstrup, Brittany Terese Fasy, Wenwen Li +4
The Gromov-Hausdorff distance measures the similarity between two metric spaces by isometrically embedding them into an ambient metric space. We introduce an analogue of this dista…
Matching distance via the extended Pareto grid
Patrizio Frosini, Eloy Mósig García, Nicola Quercioli +1
One of the most animated themes of multidimensional persistence is the comparison between invariants. The matching distance between persistent Betti numbers functions (or rank inva…
A topological model for partial equivariance in deep learning and data analysis
Lucia Ferrari, Patrizio Frosini, Nicola Quercioli +1
In this article, we propose a topological model to encode partial equivariance in neural networks. To this end, we introduce a class of operators, called P-GENEOs, that change data…
Abelian and model structures on tame functors
Wojciech Chachólski, Barbara Giunti, Claudia Landi +1
In this paper, we discuss certain circumstances in which the category of tame functors inherits an abelian category structure with minimal resolutions and a model category structur…
Geometry of the matching distance for 2D filtering functions
Marc Ethier, Patrizio Frosini, Nicola Quercioli +1
In this paper we exploit the concept of extended Pareto grid to study the geometric properties of the matching distance for -valued regular functions defined on a Rie…
Koszul complexes and relative homological algebra of functors over posets
Wojciech Chacholski, Andrea Guidolin, Isaac Ren +2
Under certain conditions, Koszul complexes can be used to calculate relative Betti diagrams of vector space-valued functors indexed by a poset, without the explicit computation of…
Realisations of posets and tameness
Wojciech Chacholski, Alvin Jin, Francesca Tombari
We introduce a construction called realisation which transforms posets into posets. We show that realisations share several key features with upper semilattices. For example, we de…
Homotopical decompositions of simplicial and Vietoris Rips complexes
Wojciech Chacholski, Alvin Jin, Martina Scolamiero +1
Motivated by applications in Topological Data Analysis, we consider decompositions of a simplicial complex induced by a cover of its vertices. We study how the homotopy type of suc…
Landscapes of data sets and functoriality of persistent homology
Wojciech Chacholski, Alessandro De Gregorio, Nicola Quercioli +1
The aim of this article is to describe a new perspective on functoriality of persistent homology and explain its intrinsic symmetry that is often overlooked. A data set for us is a…