A Symmetry-Aware Vietoris-Rips Algorithm

The typical topological data analysis pipeline starts with constructing a filtered complex – most often a Vietoris-Rips complex – from a given point cloud. The conventional algorithms tend not to assume any additional structure in the point cloud. We study whether a high degree of symmetry with a known symmetry group could bring improvements to the complex construction algorithms. By finding productive triage within a presentation of the symmetry group, preliminary results show we speed up the complex construction process. This is a joint work with Mikael Vejdemo-Johansson (CSI; CUNY GC) and Daniel Hope (CSI).