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
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Journal articles
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https://hal.archives-ouvertes.fr/hal-00923560
Contributor : Frédéric Chazal <>
Submitted on : Friday, January 3, 2014 - 11:34:35 AM
Last modification on : Friday, February 23, 2018 - 2:20:08 PM

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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⟩

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