$\delta$-core subsampling, strong collapses and TDA

TL;DR

This paper presents a novel subsampling method for topological data analysis that reduces computational complexity while preserving topological features, demonstrated through experiments on various datasets.

Contribution

Introduces a $oldsymbol{ ext{strong collapse}}$-based subsampling technique for TDA that maintains topological features with lower computational costs.

Findings

Improved persistence approximation over existing methods

Effective on both synthetic and real datasets

Reduces computational complexity significantly

Abstract

We introduce a subsampling method for topological data analysis based on strong collapses of simplicial complexes. Given a point cloud and a scale parameter $\delta$, we construct a subsampling that preserves both global and local topological features while significantly reducing computational complexity of persistent homology calculations. We illustrate the effectiveness of our approach through experiments on synthetic and real datasets, showing improved persistence approximations compared to other subsampling techniques.