Local Versus Global Distances for Zigzag Persistence Modules
Algebraic Topology
2019-03-21 v1 Computational Geometry
Abstract
This short note establishes explicit and broadly applicable relationships between persistence-based distances computed locally and globally. In particular, we show that the bottleneck distance between two zigzag persistence modules restricted to an interval is always bounded above by the distance between the unrestricted versions. While this result is not surprising, it could have different practical implications. We give two related applications for metric graph distances, as well as an extension for the matching distance between multiparameter persistence modules.
Cite
@article{arxiv.1903.08298,
title = {Local Versus Global Distances for Zigzag Persistence Modules},
author = {Ellen Gasparovic and Maria Gommel and Emilie Purvine and Radmila Sazdanovic and Bei Wang and Yusu Wang and Lori Ziegelmeier},
journal= {arXiv preprint arXiv:1903.08298},
year = {2019}
}
Comments
9 pages, 1 figure