3 papers
math.AT2025
Monoidal Rips: Stable Multiparameter Filtrations of Directed Networks
Nello Blaser, Morten Brun, Odin Hoff Gardaa +1
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…
math.AT2025
Core Bifiltration
Nello Blaser, Morten Brun, Odin Hoff Gardaa +1
The motivation of this paper is to recognize a geometric shape from a noisy sample in the form of a point cloud. Inspired by the HDBSCAN clustering algorithm, we introduce the core…
math.AT2024
The Dual Degree Cech Bifiltration
Morten Brun
In topological data analysis (TDA), a longstanding challenge is to recognize underlying geometric structures in noisy data. One motivating examples is the shape of a point cloud in…