Work

Monoidal Rips: stable multiparameter filtrations of directed networks

Year: 2026

Type: article

Abstract: We introduce the monoidal Rips filtration, a filtered simplicial set for weighted directed graphs and other lattice-valued networks. Our construction generalizes the Vietoris-Rips filtration for metric spaces by replacing the maximum operator, determining the filtration values, with a more general monoidal product. We establish interleaving guarantees for the monoidal Rips persistent homology, capturing existing stability results for real-valued networks. When the lattice is a product of totally ordered sets, we are in the setting of multiparameter persistence. Here, the interleaving distance is bounded in terms of a generalized network distance. We use this to prove a novel stability result for the sublevel Rips bifiltration. Our experimental results show that our method performs better than Flagser in a graph regression task, and that combining different monoidal products in point cloud classification can improve performance.

Source: Journal of Applied and Computational Topology

DOI: 10.1007/s41468-026-00237-z

Authors: Nello Blaser, Morten Brun, Odin Hoff Gardaa, Lars M. Salbu

Institution: University of Bergen

Language: English

Topic: Topological and Geometric Data Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,390

Funders: European Commission, Universitetet i Bergen, Haukeland Universitetssjukehus