topapprox

A Python package for persistent homology based filtering of signals over graphs and images.

Authors:
Matias de Jong van Lier, Junyan Chu, Sebastían Elías Graiff Zurita, Shizuo Kaji
Copyright © 2024

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Caution

This package is in early development. APIs are subject to change in future versions.

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Overview

topapprox implements topological filtering methods based on persistent homology, designed for:

• 1D and 2D images
• Functions defined on the nodes of a graph

It enables signal denoising and structure-preserving smoothing using techniques inspired by topological data analysis (TDA), including the Basin Hierarchy Tree (BHT).

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Documentation & Examples

• 🔗 Interactive Tutorial
• 📝 Reproducible Examples from Our Paper
• 📄 Original Paper on arXiv (2024)

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Installation

pip install git+https://github.com/mvlier/topapprox@main

Citation

If you use this package in your work, please cite:

Matias de Jong van Lier, Sebastían Elías Graiff Zurita, Shizuo Kaji.
Topological filtering of a signal over a network (2024).
arXiv:2408.14109

@article{vanlier2024topological,
  title={Topological filtering of a signal over a network},
  author={de Jong van Lier, Matias and Graiff Zurita, Sebastían Elías and Kaji, Shizuo},
  journal={arXiv preprint arXiv:2408.14109},
  year={2024}
}