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Persistent homology studies the evolution of k-holes along a "filtration". The persistence barcode encodes birth and death times of k-holes along such filtration. k-Holes with short lifetimes are “topological noise”, and those with long lifetimes are “topological features” associated to the filtration. Persistent entropy is defined as the Shannon entropy of the persistence barcode. We will present properties of persistent entropy and derive a method for separating noise from features given a persistent barcode.
This presentation is part of Minisymposium “MS16 - Topological Image Analysis: Methods, Algorithms, Applications (3 parts)”
organized by: Patrizio Frosini (University of Bologna) , Massimo Ferri (University of Bologna) , Claudia Landi (University of Modena and Reggio Emilia) .