arXiv：cs.LG· Matt\'eo Cl\'emot, Julie Digne, Julien Tierny·· 6 小时前AI 评分33
sublevel Flood 双滤流：面向可扩展的 2 参数持续同调
The sublevel Flood bifiltration: towards scalable 2-parameter persistent homology
AI 导读
研究者提出 sublevel Flood bifiltration，一种在大型点集上高效计算 2 参数持续同调的新方法，可对 sublevel offset bifiltration 做可扩展近似。该构造扩展自单参数持续同调的 Flood filtration，具有理论稳定性，并在密度敏感的低维合成数据集及真实时间序列分类任务上验证了性能。
正文
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.
| Subjects: | Algebraic Topology (math.AT); Computational Geometry (cs.CG); Machine Learning (cs.LG) |
| Cite as: | arXiv:2610.05441 [math.AT] |
| (or arXiv:2610.05441v2 [math.AT] for this version) | |
| https://doi.org/10.48550/arXiv.2610.05441 arXiv-issued DOI via DataCite |
Submission history
From: Mattéo Clémot [view email]
[v1]
Sun, 4 Oct 2026 18:22:32 UTC (1,921 KB)
[v2]
Wed, 7 Oct 2026 15:12:36 UTC (1,921 KB)
来源：arXiv：cs.LG · arxiv.org