2014/02/19 by Andrea Cerri, Patrizio Frosini · 7 citations
Computer Science · Biochemistry, Genetics and Molecular Biology · Mathematics · #Topological and Geometric Data Analysis #Single-cell and spatial transcriptomics #Betti number #Mathematics #Topological data analysis #Classification of discontinuities #Context (archaeology) #Pareto principle #Persistence (discontinuity) #Representation (politics) #Extension (predicate logic) #Persistent homology #Topology (electrical circuits) #Mathematical optimization #Discrete mathematics #Algorithm #Combinatorics #Computer science #Mathematical analysis
paper · doi:10.1002/mma.3093
published in Mathematical Methods in the Applied Sciences 38(4), 617-629 (Wiley)
openalex publication_date 2014/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/08
Abstract Topological persistence has proven to be a promising framework for dealing with problems concerning the analysis of data. In this context, it was originally introduced by taking into account 1‐dimensional properties of data, modeled by real‐valued functions. More recently, topological persistence has been generalized to consider multidimensional properties of data, coded by vector‐valued functions. This extension enables the study of multidimensional persistent Betti numbers , which provide a representation of data based on the properties under examination. In this contribution, we establish a new link between multidimensional topological persistence and Pareto optimality, proving that discontinuities of multidimensional persistent Betti numbers are necessarily pseudocritical or special values of the considered functions. Copyright © 2014 John Wiley & Sons, Ltd.