2020/05/06 by Alessandro De Gregorio, Ulderico Fugacci, De Gregorio, Alessandro +5
Computer Science · Mathematics · #54E35 #55N31 #62R40 #Algebraic Topology (math.AT) #FOS: Mathematics #General Topology (math.GN) #Geometric Analysis and Curvature Flows #Homotopy and Cohomology in Algebraic Topology #Metric Geometry (math.MG) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2005.03109
openalex publication_date 2020/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Finite metric spaces are the object of study in many data analysis problems. We examine the concept of weak isometry between finite metric spaces, in order to analyse properties of the spaces that are invariant under strictly increasing rescaling of the distance functions. In this paper, we analyse some of the possible complete and incomplete invariants for weak isometry and we introduce a dissimilarity measure that asses how far two spaces are from being weakly isometric. Furthermore, we compare these ideas with the theory of persistent homology, to study how the two are related.