Stable Volumes for Persistent Homology
Abstract
This paper proposes a stable volume and a stable volume variant, referred to as a stable sub-volume, for more reliable data analysis using persistent homology. In prior research, an optimal cycle and similar ideas have been proposed to identify the homological structure corresponding to each birth-death pair in a persistence diagram. While this is helpful for data analysis using persistent homology, the results are sensitive to noise. In this paper, stable volumes and stable sub-volumes are proposed to solve this problem. For a special case, we prove that a stable volume is the robust part of an optimal volume against noise. We implemented stable volumes and sub-volumes on HomCloud, a data analysis software package based on persistent homology, and show examples of stable volumes and sub-volumes.
Cite
@article{arxiv.2109.11711,
title = {Stable Volumes for Persistent Homology},
author = {Ippei Obayashi},
journal= {arXiv preprint arXiv:2109.11711},
year = {2022}
}