Certified Mapper: Repeated testing for acyclicity and obstructions to the nerve lemma
Abstract
The Mapper algorithm does not include a check for whether the cover produced conforms to the requirements of the nerve lemma. To perform a check for obstructions to the nerve lemma, statistical considerations of multiple testing quickly arise. In this paper, we propose several statistical approaches to finding obstructions: through a persistent nerve lemma, through simulation testing, and using a parametric refinement of simulation tests. We suggest Certified Mapper -- a method built from these approaches to generate certificates of non-obstruction, or identify specific obstructions to the nerve lemma -- and we give recommendations for which statistical approaches are most appropriate for the task.
Cite
@article{arxiv.1808.09933,
title = {Certified Mapper: Repeated testing for acyclicity and obstructions to the nerve lemma},
author = {Mikael Vejdemo-Johansson and Alisa Leshchenko},
journal= {arXiv preprint arXiv:1808.09933},
year = {2018}
}
Comments
16 pages, submitted to the proceedings of the Abel symposium