Weighted Persistent Homology
Algebraic Topology
2019-05-29 v2
Abstract
We introduce weighted versions of the classical \v{C}ech 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.
Cite
@article{arxiv.1709.00097,
title = {Weighted Persistent Homology},
author = {Greg Bell and Austin Lawson and Joshua Martin and James Rudzinski and Clifford Smyth},
journal= {arXiv preprint arXiv:1709.00097},
year = {2019}
}
Comments
11 pages, 5 figures