Topological Correlation
Algebraic Topology
2025-06-23 v1 Computational Geometry
Abstract
We introduce two novel concepts, topological difference and topological correlation, that offer a new perspective on the discriminative power of multiparameter persistence. The former quantifies the discrepancy between multiparameter and monoparameter persistence, while the other leverages this gap to measure the interdependence of filtering functions. Our framework sheds light on the expressive advantage of multiparameter over monoparameter persistence and suggests potential applications.
Cite
@article{arxiv.2506.16985,
title = {Topological Correlation},
author = {Isabella Mastroianni and Ulderico Fugacci},
journal= {arXiv preprint arXiv:2506.16985},
year = {2025}
}