PETLS: PErsistent Topological Laplacian Software

TL;DR

PETLS is a C++/Python software library that efficiently computes persistent topological Laplacians, providing multiscale geometric insights for topological data analysis in machine learning.

Contribution

It introduces a flexible framework and novel algorithms for persistent topological Laplacians, with an efficient implementation interfacing multiple complexes.

Findings

Efficient computation of persistent Betti numbers and eigenvalues.

Supports various complexes like simplicial, alpha, and cellular Sheaf.

Provides practical recommendations for data analysis applications.

Abstract

Persistent topological Laplacians are operators that provide persistent Betti numbers and additional multiscale geometric information through the eigenvalues of the persistent topological Laplacian matrix. We introduce a framework and novel algorithm to aid in the computation of persistent topological Laplacians. We implement existing and new persistent Laplacian algorithms in an efficient and flexible C++ library with Python bindings, titled PETLS: PErsistent Topological Laplacian Software. As part of this library, we interface with several complexes commonly used in topological data analysis (TDA), such as simplicial, alpha, directed flag, Dowker, and cellular Sheaf. Because increased efficiency broadens the set of computationally feasible applications, we provide recommendations on how to use algorithms and complexes for data analysis in machine learning.