velour 2020.11.18

Topological inference from point clouds with persistent homology

velour

Python package for topological inference from point clouds with persistent homology. Based on the gudhi library.

Methods

The package velour gathers implementations of our methods for topological inference. It allows the use of:

• DTM-filtrations: a family of filtrations for persistent homology, that can be applied even when the input point cloud contains anomalous points. Notebook demo here and mathematical explanation here.
• Lifted sets and lifted filtrations: allows to estimate the homology of an abstract manifold from a finite sample of an immersion of it. Notebook demo here and mathematical explanation here.
• Persistent Stiefel-Whitney classes: allows to estimate the first Stiefel-Whitney class of a vector bundle from a finite sample of it. Notebook demo here and mathematical explanation here.

Structure

The package is divided into three modules:

• persistent gathers tools for handling filtrations of simplicial complexes (simplex trees).
• geometry contains the implementation of various geometric quantities used by persistent.
• datasets consists in various utilities for sampling datasets (from $\mathbb{R}^2$ to $\mathbb{R}^{12}$) and plotting them.

Setup

It can be installed from PyPI via

pip install velour

Current release: 2020.11.18

Documentation

Not yet! But feel free to contact me anytime.

Raphaël Tinarrage - https://raphaeltinarrage.github.io/