Persistence stability for geometric complexes

被引：125

作者：

Chazal, Frederic ^{[1
]}

de Silva, Vin ^{[2
]}

Oudot, Steve ^{[1
]}

机构：

[1] INRIA Saclay, Palaiseau, France

[2] Pomona Coll, Claremont, CA 91711 USA

来源：

GEOMETRIAE DEDICATA | 2014年 / 173卷 / 01期

基金：

美国国家科学基金会;

关键词：

Persistent homology; Vietoris-Rips complex; Cech complex; Gromov-Hausdorff distance; METRIC-SPACES;

D O I：

10.1007/s10711-013-9937-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we study the properties of the homology of different geometric filtered complexes (such as Vietoris-Rips, ech 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 ech complexes built on top of compact spaces.

引用

页码：193 / 214

页数：22

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