Critical Points to Determine Persistence Homology

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.