Weighted Persistent Homology

Abstract

We introduce weighted versions of the classical Čech and Vietoris-Rips complexes. We show that a version of the Vietoris-Rips Lemma holds for these weighted complexes and that they enjoy appropriate stability properties. We also give some preliminary applications of these weighted complexes.

11 pages, 5 figures

References in corpus (1)

• Metrics for generalized persistence modules

Cited by in corpus (2)

• Computing persistent Stiefel-Whitney classes of line bundles
• Detection of Small Holes by the Scale-Invariant Robust Density-Aware Distance (RDAD) Filtration