Computation of degree-1 persistent homology on larger point-clouds using the Reduced Vietoris-Rips filtration

Abstract

Computing Persistent Homology for large point clouds remains a bottleneck for the wider adoption of persistent homology by the scientific community. We present an algorithm which can compute the degree-1 Vietoris-Rips Persistent Homology of point clouds in low dimensional Euclidean Space for larger point clouds.

54 pages, 19 figures, 5 tables