The reflection distance between zigzag persistence modules
Algebraic Topology
2019-07-02 v3 Computational Geometry
Abstract
By invoking the reflection functors introduced by Bernstein, Gelfand, and Ponomarev in 1973, in this paper we define a metric on the space of all zigzag modules of a given length, which we call the reflection distance. We show that the reflection distance between two given zigzag modules of the same length is an upper bound for the -bottleneck distance between their respective persistence diagrams.
Keywords
Cite
@article{arxiv.1805.11190,
title = {The reflection distance between zigzag persistence modules},
author = {Alexander Elchesen and Facundo Mémoli},
journal= {arXiv preprint arXiv:1805.11190},
year = {2019}
}
Comments
30 pages, 2 figures. Final version; to appear in the Journal of Applied and Computational Topology