Robert J. Adler, Omer Bobrowski, Matthew S. Borman, Eliran Subag, Shmuel Weinberger
Published 2010-03-04, updated 2010-03-26Version 2
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.
On the persistent homology of almost surely $C^0$ stochastic processes
Continuity of Random Fields on Riemannian Manifolds
Crackle: The Persistent Homology of Noise
![QR code for arXiv:1003.1001 [math.PR]](http://oss.arxitics.com/images/favicon.svg)