A statistical approach to persistent homology
Peter Bubenik, Peter T. Kim · Homology Homotopy and Applications · 2007
Assume that a finite set of points is randomly sampled from a subspace of a metric space.Recent advances in computational topology have provided several approaches to recovering the geometric and topological properties of the underlying space.In this paper we take a statistical approach to this problem.We assume that the data is randomly sampled from an unknown probability distribution.We define two filtered complexes with which we can calculate the persistent homology of a probability distribution.Using statistical estimators for samples from certain families of distributions, we show that we can recover the persistent homology of the underlying distribution.