Persistent homology is a method for probing topological properties of point clouds and functions. The method involves tracking the birth and death of topological features (2000) as one varies a tuning parameter. Features with short lifetimes are informally considered to be "topological noise," and those with a long lifetime are considered to be "topological signal." In this paper, we bring some statistical ideas to persistent homology. In particular, we derive confidence sets that allow us to separate topological signal from topological noise.
arXiv comments
Published in at http://dx.doi.org/10.1214/14-AOS1252 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
Journal reference
Annals of Statistics 2014, Vol. 42, No. 6, 2301-2339
Just a few days ago the following paper was published on the ArXiv, it specifically tackles the problem of noise. I haven't had time to read it thoroughly, but it also contains a nice introduction to persistent homology for statisticians, who are usually not familiar with the…
Just a few days ago the following paper was published on the ArXiv, it specifically tackles the problem of noise. I haven't had time to read it thoroughly, but it also contains a nice introduction to persistent homology for statisticians, who are usually not familiar with the…
otView on HNParent context
A good idea. This helps so that when the paper is updated one finds the most current version. http://arxiv.org/abs/1303.7117
nkurzView on HNParent context