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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

   

 

Barcodes: The persistent topology of data


Author: Robert Ghrist
Journal: Bull. Amer. Math. Soc. 45 (2008), 61-75
MSC (2000): Primary 55N35; Secondary 62H35
Published electronically: October 26, 2007
MathSciNet review: 2358377
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

Robert Ghrist
Affiliation: Department of Mathematics and Coordinated Science Laboratory, University of Illinois, Urbana, Illinois 61801

DOI: http://dx.doi.org/10.1090/S0273-0979-07-01191-3
PII: S 0273-0979(07)01191-3
Received by editor(s): May 16, 2007
Received by editor(s) in revised form: July 4, 2007
Published electronically: October 26, 2007
Additional Notes: This article is based on the lecture presented at the January 2007 national meeting of the AMS in New Orleans. The author gratefully acknowledges the support of DARPA #HR0011-07-1-0002 and the helpful comments of G. Carlsson, V. de Silva, and A. Zomorodian. The work reviewed in this article is funded by the DARPA program TDA: Topological Data Analysis.
Article copyright: © Copyright 2007 Robert W. Ghrist