2025/04/16 by Aziz Burak Gülen, Gülen, Aziz Burak, Facundo Mémoli +3 · 1 citation
Computer Science · Mathematics · #Algebraic Topology (math.AT) #Digital Image Processing Techniques #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2504.11694
openalex publication_date 2025/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the concept of weighted persistence diagrams and develop a functorial pipeline for constructing them from finite metric measure spaces. This builds upon an existing functorial framework for generating classical persistence diagrams from finite pseudo-metric spaces. To quantify differences between weighted persistence diagrams, we define the p-edit distance for p∈ [1,∞], and-focusing on the weighted Vietoris-Rips filtration-we establish that these diagrams are stable with respect to the p-Gromov-Wasserstein distance as a direct consequence of functoriality. In addition, we present an Optimal Transport-inspired formulation of the p-edit distance, enhancing its conceptual clarity. Finally, we explore the discriminative power of weighted persistence diagrams, demonstrating advantages over their unweighted counterparts.