Core Bifiltration [arXiv]

This repository contains an implementation of alpha-core and core Čech persistent homology, together with Jupyter notebooks demonstrating its application to noisy point cloud data.

Get Started

Install dependencies by running pip install -r requirements.txt if needed.

Run the notebook example_usage.ipynb for an demonstration of the application of core Čech and alpha-core persistent homology to noisy point clouds. This notebook contains examples for computing persistence along a line and for a fixed $k$.

To reproduce the experiments presented in the paper with $\beta=1$, run the notebook run_experiments.ipynb. To reproduce the experiments examining different values of $\beta$, run the notebook run_experiments_beta.ipynb.

Other Files

The code for constructing the filtered nerves is contained in core.py. The functions core_cech and core_alpha returns a simplex tree (a gudhi.SimplexTree instance) representing the core Čech and alpha-core filtered nerves, respectively. Different point cloud dataset generators used in the notebooks can be found in datasets.py.