Stable Invariants for Multiparameter Persistence
Algebraic Topology
2021-04-15 v3
Abstract
In this paper we explain how to convert discrete invariants into stable ones via what we call hierarchical stabilization. We illustrate this process by constructing stable invariants for multi-parameter persistence modules with respect to the interleaving distance and so called simple noise systems. For one parameter, we recover the standard barcode information. For more than one parameter we prove that the constructed invariants are in general NP-hard to calculate. A consequence is that computing the feature counting function, proposed by Scolamiero et. al. (2016), is NP-hard.
Cite
@article{arxiv.1703.03632,
title = {Stable Invariants for Multiparameter Persistence},
author = {Oliver Gäfvert and Wojciech Chachólski},
journal= {arXiv preprint arXiv:1703.03632},
year = {2021}
}