Persistence stability for geometric complexes
Persistence stability for geometric complexes
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DOI：
10.1007/s10711-013-9937-z
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发表时间：
2014-12-01
影响因子：
0.5
通讯作者：
Oudot, Steve
中科院分区：
文献类型：
--
作者：
Chazal, Frederic;de Silva, Vin;Oudot, Steve
本文研究了建立在完全有界度量空间上的不同几何滤子复形（如Vietoris-Rips、ech和witness复形）的同调性质。利用拓扑持久性理论的最新发展，我们提供了简单而自然的证明，这种复合物的持久同源性的稳定性相对于Gromov-Hausdorff距离。我们还展示了一些值得注意的性质的同源性的RIP和ech复合物建立在紧凑的空间。
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.