HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Journal articles

Persistence Stability for Geometric complexes

Frédéric Chazal 1 Vin de Silva 2 Steve Y. Oudot 1
1 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
2 Department of Mathematics - Pomona College
Abstract : In this paper we study the properties of the homology of different geometric filtered complexes (such as Vietoris–Rips, Cech and witness complexes) built on top of totally bounded metric spaces. Using recent developments in the theory of topological persistence, we provide simple and natural proofs of the stability of the persistent homology of such complexes with respect to the Gromov–Hausdorff distance. We also exhibit a few noteworthy properties of the homology of the Rips and Cech complexes built on top of compact spaces.
Keywords : Persistent homology Vietoris-Rips complex Cech complex Gromov-Hausdorff distance
Document type :
Journal articles
Complete list of metadata
https://hal.archives-ouvertes.fr/hal-00923560
Contributor : Frédéric Chazal Connect in order to contact the contributor
Submitted on : Friday, January 3, 2014 - 11:34:35 AM
Last modification on : Thursday, January 20, 2022 - 5:32:58 PM

Links full text

arxiv

Identifiers

Collections

INRIA | INSMI | INRIA2

Citation

Frédéric Chazal, Vin de Silva, Steve Y. Oudot. Persistence Stability for Geometric complexes. Geometriae Dedicata, Springer Verlag, 2014, 173, pp.193-214. ⟨10.1007/s10711-013-9937-z⟩. ⟨hal-00923560⟩

Export

BibTeX TEI DC DCterms EndNote Datacite

Share

Metrics

Record views

181