2025/06/20 by Mastroianni, Isabella, Fugacci, Ulderico
Biochemistry, Genetics and Molecular Biology · Computer Science · #Algebraic Topology (math.AT) #Cell Image Analysis Techniques #Computational Geometry (cs.CG) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning and Data Classification #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2506.16985
openalex publication_date 2025/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.