Topological Correlation

TL;DR

This paper introduces topological difference and correlation to analyze the discriminative power of multiparameter persistence, highlighting its advantages over monoparameter methods and suggesting new applications.

Contribution

It presents novel concepts for quantifying the gap between multiparameter and monoparameter persistence, providing insights into their interdependence and expressive capabilities.

Findings

Topological difference quantifies the discrepancy between persistence types.

Topological correlation measures the interdependence of filtering functions.

Framework demonstrates the expressive advantage of multiparameter persistence.

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.