Barcodes: The persistent topology of data

Ghrist, Robert

doi:10.1090/S0273-0979-07-01191-3

Author: Robert Ghrist
Journal: Bull. Amer. Math. Soc. 45 (2008), 61-75
MSC (2000): Primary 55N35; Secondary 62H35
DOI: https://doi.org/10.1090/S0273-0979-07-01191-3
Published electronically: October 26, 2007
MathSciNet review: 2358377
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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.

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