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

arXiv: https://arxiv.org/abs/2610.05441 · HTML: https://mlsanity.com/paper/2610.05441/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 37 of its 63 references that are in the map.
- First posted on arXiv 4 Oct 2026.

## Builds on (most cited first, 30 of 37)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [The UCR Time Series Archive](https://mlsanity.com/paper/1810.07758/) (2018)
- [An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists](https://mlsanity.com/paper/1710.04019/) (2017)
- [Topological Autoencoders](https://mlsanity.com/paper/1906.00722/) (2019)
- [Ripser: efficient computation of Vietoris-Rips persistence barcodes](https://mlsanity.com/paper/1908.02518/) (2019)
- [A Stable Multi-Scale Kernel for Topological Machine Learning](https://mlsanity.com/paper/1412.6821/) (2014)
- [PVT: Point-Voxel Transformer for Point Cloud Learning](https://mlsanity.com/paper/2108.06076/) (2021)
- [Learning Topology-Preserving Data Representations](https://mlsanity.com/paper/2302.00136/) (2023)
- [GPU-Accelerated Computation of Vietoris-Rips Persistence Barcodes](https://mlsanity.com/paper/2003.07989/) (2020)
- [Robust Topological Inference: Distance To a Measure and Kernel Distance](https://mlsanity.com/paper/1412.7197/) (2014)
- [Interactive Visualization of 2-D Persistence Modules](https://mlsanity.com/paper/1512.00180/) (2015)
- [An Introduction to Multiparameter Persistence](https://mlsanity.com/paper/2203.14289/) (2022)
- [A Kernel for Multi-Parameter Persistent Homology](https://mlsanity.com/paper/1809.10231/) (2018)
- [Persistent Topological Features in Large Language Models](https://mlsanity.com/paper/2410.11042/) (2024)
- [giotto-ph: A Python Library for High-Performance Computation of Persistent Homology of Vietoris-Rips Filtrations](https://mlsanity.com/paper/2107.05412/) (2021)
- [Graphcode: Learning from multiparameter persistent homology using graph neural networks](https://mlsanity.com/paper/2405.14302/) (2024)
- [A Framework for Fast and Stable Representations of Multiparameter Persistent Homology Decompositions](https://mlsanity.com/paper/2306.11170/) (2023)
- [Stability and Machine Learning Applications of Persistent Homology Using the Delaunay-Rips Complex](https://mlsanity.com/paper/2303.01501/) (2023)
- [The Flood Complex: Large-Scale Persistent Homology on Millions of Points](https://mlsanity.com/paper/2509.22432/) (2025)
- [The Morse theory of vCech and Delaunay complexes](https://mlsanity.com/paper/1312.1231/) (2013)
- [Stability of 2-Parameter Persistent Homology](https://mlsanity.com/paper/2010.09628/) (2020)
- [The Shape of Adversarial Influence: Characterizing LLM Latent Spaces with Persistent Homology](https://mlsanity.com/paper/2505.20435/) (2025)
- [Computing the Multicover Bifiltration](https://mlsanity.com/paper/2103.07823/) (2021)
- [Multi-parameter Module Approximation: an efficient and interpretable invariant for multi-parameter persistence modules with guarantees](https://mlsanity.com/paper/2206.02026/) (2022)
- [Delaunay Bifiltrations of Functions on Point Clouds](https://mlsanity.com/paper/2310.15902/) (2023)
- [Computing the interleaving distance is NP-hard](https://mlsanity.com/paper/1811.09165/) (2018)
- [Exact computation of the matching distance on 2-parameter persistence modules](https://mlsanity.com/paper/1812.09085/) (2018)
- [Combinatorial presentation of multidimensional persistent homology](https://mlsanity.com/paper/1409.7936/) (2014)
- [Efficient Approximation of the Matching Distance for 2-parameter persistence](https://mlsanity.com/paper/1912.05826/) (2019)

## Abstract (arXiv)

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.