Barcodes: The persistent topology of data
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
Full-text PDF Free Access
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
MR Author ID:
346210
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