Applied topology 14: Cech and Vietoris-Rips simplicial complexes
Abstract: We describe Cech and Vietoris-Rips simplicial complexes, which are the two most common ways to build an increasing sequence of simplicial complexes on top of point cloud data, in order to measure the shape of that dataset via persistent homology.
This video accompanies the class "Topological Data Analysis" at Colorado State University:
https://www.math.colostate.edu/~adams/teaching/dsci475spr2021/