Subsampling Methods for Persistent Homology
Algebraic Topology
2014-06-10 v1 Computational Geometry
Applications
Abstract
Persistent homology is a multiscale method for analyzing the shape of sets and functions from point cloud data arising from an unknown distribution supported on those sets. When the size of the sample is large, direct computation of the persistent homology is prohibitive due to the combinatorial nature of the existing algorithms. We propose to compute the persistent homology of several subsamples of the data and then combine the resulting estimates. We study the risk of two estimators and we prove that the subsampling approach carries stable topological information while achieving a great reduction in computational complexity.
Cite
@article{arxiv.1406.1901,
title = {Subsampling Methods for Persistent Homology},
author = {Frédéric Chazal and Brittany Terese Fasy and Fabrizio Lecci and Bertrand Michel and Alessandro Rinaldo and Larry Wasserman},
journal= {arXiv preprint arXiv:1406.1901},
year = {2014}
}