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.
Information
Published: 1 January 2010
First available in Project Euclid: 26 October 2010
MathSciNet: MR2798515
Digital Object Identifier: 10.1214/10-IMSCOLL609
Subjects:
Primary:
55N35
,
60G15
Secondary:
60G55
,
62H35
Keywords:
barcodes
,
Betti numbers
,
Euler characteristic
,
Gaussian kinematic formula
,
Gaussian processes
,
manifold learning
,
Persistent homology
,
random complexes
,
Random fields
Rights: Copyright © 2010, Institute of Mathematical Statistics
