Article,
Barcodes: The persistent topology of data
Bulletin of the American Mathematical Society, (2008)
DOI: 10.1090/S0273-0979-07-01191-3
Abstract
This article surveys recent work of Carlsson and collaborators on applications of computational algebraic topology to problems of feature detection and shape recognition in high-dimensional data. The primary mathematical tool considered is a homology theory for point-cloud data sets--persistent homology--and a novel representation of this algebraic characterization--barcodes. We sketch an application of these techniques to the classification of natural images.
