Computing Persistent Homology with Various Coefficient Fields in a Single Pass - Archive ouverte HAL Access content directly
Conference Papers Year : 2014

Computing Persistent Homology with Various Coefficient Fields in a Single Pass

(1) , (1)
1
Jean-Daniel Boissonnat
  • Function : Author
  • PersonId : 830857
Clément Maria
  • Function : Author
  • PersonId : 926304

Abstract

This article introduces an algorithm to compute the persistent homology of a filtered complex with various coefficient fields in a single matrix reduction. The algorithm is output-sensitive in the total number of distinct persistent homological features in the diagrams for the different coefficient fields. This computation allows us to infer the prime divisors of the torsion coefficients of the integral homology groups of the topological space at any scale, hence furnishing a more informative description of topology than persistence in a single coefficient field. We provide theoretical complexity analysis as well as detailed experimental results. The code is part of the Gudhi library.
On introduit un algorithme de calcul de l'homologie persistante d'un complexe filtré sur plusieurs corps en n'utilisant qu'une seule réduction de matrice. On obtient ainsi, sans coût supplémentaire,de l'information sur les coefficients de torsion. L'algorithme a été programmé et le code fait partie de la bibliothèque Gudhi.
Fichier principal
Vignette du fichier
main.pdf (381.08 Ko) Télécharger le fichier
Vignette du fichier
main_esa-figure0.png (32.16 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Format : Figure, Image
Loading...

Dates and versions

hal-01022669 , version 1 (10-07-2014)

Identifiers

  • HAL Id : hal-01022669 , version 1

Cite

Jean-Daniel Boissonnat, Clément Maria. Computing Persistent Homology with Various Coefficient Fields in a Single Pass. European Symposium on Algorithms, European Association for Theoretical Computer Science (EATCS), Sep 2014, Wrocław, Poland. ⟨hal-01022669⟩

Collections

INRIA INRIA2
131 View
178 Download

Share

Gmail Facebook Twitter LinkedIn More