Vietoris-Rips complex for n-dimensional point cloud

data_science

#1

I am studying about Vietoris-Rips complexes, and I have some doubt regarding the dimension of the spheres (balls) involved in its construction. For example, is it so that for a point cloud with 2D points we have a circle, for a 3D point cloud we have a 3-sphere,…and for n-dimensional point cloud we need a hyberball or n-sphere?