Persistent Homology for Random Fields and Complexes
Probability
2015-03-13 v2 Algebraic Topology
Abstract
We discuss and review recent developments in the area of applied algebraic topology, such as persistent homology and barcodes. In particular, we discuss how these are related to understanding more about manifold learning from random point cloud data, the algebraic structure of simplicial complexes determined by random vertices, and, in most detail, the algebraic topology of the excursion sets of random fields.
Cite
@article{arxiv.1003.1001,
title = {Persistent Homology for Random Fields and Complexes},
author = {Robert J. Adler and Omer Bobrowski and Matthew S. Borman and Eliran Subag and Shmuel Weinberger},
journal= {arXiv preprint arXiv:1003.1001},
year = {2015}
}