Necessary conditions for discontinuities of multidimensional persistent Betti numbers |
| |
| Authors: | Andrea Cerri Patrizio Frosini |
| |
| Affiliation: | 1. CNR – IMATI via de Marini 6, I‐16149 Genova, Italy;2. Dipartimento di Matematica, Università di Bologna, P.zza di Porta S. Donato 5, I‐40126 Bologna, Italy |
| |
| 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. |
| |
| Keywords: | topological persistence foliation method Pareto optimality |
|
|
