Geometric Approaches on Persistent Homology
Algebraic Topology
2022-12-27 v3 Computational Geometry
Geometric Topology
Abstract
We introduce several geometric notions, including the width of a homology class, to the theory of persistent homology. These ideas provide geometric interpretations of persistence diagrams. Indeed, we give quantitative and geometric descriptions of the "life span" or "persistence" of a homology class. As a case study, we analyze the power filtration on unweighted graphs, and provide explicit bounds for the life spans of homology classes in persistence diagrams in all dimensions.
Cite
@article{arxiv.2103.06408,
title = {Geometric Approaches on Persistent Homology},
author = {Henry Adams and Baris Coskunuzer},
journal= {arXiv preprint arXiv:2103.06408},
year = {2022}
}