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Barcodes: The persistent topology of data
Author(s):
Robert
Ghrist
Journal:
Bull. Amer. Math. Soc.
45
(2008),
61-75.
MSC (2000):
Primary 55N35;
Secondary 62H35
Posted:
October 26, 2007
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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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Additional Information:
Robert
Ghrist
Affiliation:
Department of Mathematics and Coordinated Science Laboratory, University of Illinois, Urbana, Illinois 61801
DOI:
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
Posted:
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.
Copyright of article:
Copyright
2007,
Robert W. Ghrist
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