Abstract

Vietoris-Rips persistent homology is a widely used type of persistent homology to analyse the shape of point clouds. In particular, degree-1 Vietoris-Rips persistent homology is useful for detecting loop structures in space, but comes with the drawback of being computationally too expensive to apply to the large data sets encountered in the modern world. We present a modified version of the standard reduction algorithm for point clouds in Euclidean space and show the results for code optimised to compute degree-1 persistent homology for point clouds in 2 and 3 dimensional Euclidean space.