Critical Points to Determine Persistence Homology
This addresses efficiency in topological data analysis for domain-specific applications like image classification, but it is incremental as it builds on existing sampling and persistence methods.
The paper tackles the computational burden of persistence homology on large point clouds by sampling critical points of a Morse function to approximate simplicial complexes, achieving comparable classification accuracy to farthest point sampling in an ethnicity classification task on human face images.
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.