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

This repository contains the code for the manuscript Sublevel Flood bifiltration: scalable 2-parameter persistent homology. The aim is to provide a way to compute 2-parameter persistent homology of large scale point clouds (up to $10^6$). To do so, it extends the Flood filtration to the 2-parameter context.

The Python package constructs a SimplexTreeMulti from the multipers library.

Installation

sublevel-flood can be installed via PyPI.

pip install sublevel-flood

Usage

The following example computes the sublevel Flood bifiltration (with 100 landmarks) of a point set in $\mathbb{R}^3$ distributed as a sphere with ambient noise, using CUDA. Then, it computes and plots its multiparameter module approximation with multipers.

import slflood
from slflood.data import noisy_sphere_data

import matplotlib.pyplot as plt
import multipers

n_pts = 10000
n_lms = 100
dim = 3

pts, lms_idx, fun = noisy_sphere_data(n_pts, n_lms, dim,
                                      bandwidth=0.2)

slf = slflood.slflood_bifiltration(pts.cuda(), lms_idx.cuda(), fun.cuda())
mma = multipers.module_approximation(slf)
mma.plot(box=[[0, 0], [1, 1]])
plt.show()

Citation

@inproceedings{clemot2026sublevel,
      title={The sublevel {Flood} bifiltration: towards scalable 2-parameter persistent homology}, 
      author={Cl{\'e}mot, Matt{\'e}o and Digne, Julie and Tierny, Julien},
      year={2026},
      booktitle={NeurIPS},
}