The sublevel Flood bifiltration: towards scalable 2-parameter persistent homology

Abstract:Multiparameter persistent homology is a rapidly developing branch of topological data analysis that improves the robustness of single-parameter persistent homology to outliers, while still capturing the metric characteristics of the data. However, a notable limitation is its lack of scalability. In this paper, we introduce a novel approach for efficiently computing 2-parameter persistent homology on large point sets. Our work extends the Flood filtration, originally developed for single-parameter persistence. Our construction, called the sublevel Flood bifiltration, offers a scalable approximation of the sublevel offset bifiltration. We show that it benefits from theoretical stability properties and describe how to compute it efficiently. We demonstrate the performance of our approach in classification tasks on low-dimensional synthetic datasets, where density awareness is critical, as well as on real-world time series datasets.

Algebraic Topology (math.AT); Computational Geometry (cs.CG); Machine Learning (cs.LG)

arXiv:2610.05441 [math.AT]

(or arXiv:2610.05441v1 [math.AT] for this version)

https://doi.org/10.48550/arXiv.2610.05441 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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