Critical Points to Determine Persistence Homology

TL;DR

This paper introduces a novel sampling method based on critical points of Morse functions to efficiently approximate complexes for persistence homology, improving classification of face images by reducing computational costs.

Contribution

It proposes a new critical point sampling technique for persistence homology that outperforms traditional methods like farthest point sampling in image classification tasks.

Findings

Critical point sampling effectively approximates complexes for persistence homology.

The method improves classification accuracy of face images into ethnic groups.

It reduces computational complexity compared to existing sampling techniques.

Abstract

Computation of the simplicial complexes of a large point cloud often relies on extracting a sample, to reduce the associated computational burden. The study considers sampling critical points of a Morse function associated to a point cloud, to approximate the Vietoris-Rips complex or the witness complex and compute persistence homology. The effectiveness of the novel approach is compared with the farthest point sampling, in a context of classifying human face images into ethnics groups using persistence homology.