Eulearning: Euler characteristic tools for topological data analysis

Authors: Olympio Hacquard and Vadim Lebovici

Description

eulearning is a Python package to compute Euler characteristic profiles of multi-parameter filtrations, as well as their Radon and hybrid transforms. Please find short usage demonstrations in the notebooks of the demos/ folder.

• descriptors.py contains the scikit-learn transformers computing Euler characteristic tools.

• datasets.py contains all datasets used in our article, at the exception of graph datasets which come from here and can be downloaded at the right format from the Perslay repository. One graph dataset is included for a demo.

• utils.py contains auxilary but necessary functions. For instance, in contains a way to compute multi-parameter filtrations in the form of vectorized simplex trees.

Package requirements

For Euler characteristic descriptors: numpy, scikit-learn.

For multi-parameter filtrations: numba, scipy, GraphRicciCurvature.

For datasets: Gudhi, tadasets. Moreover, we use code from Guillaume Moroz's repository dpp to generate Ginibre and Poisson point clouds.

For demos: xgboost, matplotlib.