Metrics for generalized persistence modules
Abstract
We consider the question of defining interleaving metrics on generalized persistence modules over arbitrary preordered sets. Our constructions are functorial, which implies a form of stability for these metrics. We describe a large class of examples, inverse-image persistence modules, which occur whenever a topological space is mapped to a metric space. Several standard theories of persistence and their stability can be described in this framework. This includes the classical case of sublevelset persistent homology. We introduce a distinction between `soft' and `hard' stability theorems. While our treatment is direct and elementary, the approach can be explained abstractly in terms of monoidal functors.
Cite
@article{arxiv.1312.3829,
title = {Metrics for generalized persistence modules},
author = {Peter Bubenik and Vin de Silva and Jonathan Scott},
journal= {arXiv preprint arXiv:1312.3829},
year = {2016}
}
Comments
Final version; no changes from previous version. Published online Oct 2014 in Foundations of Computational Mathematics. Print version to appear