Barcodes: The persistent topology of data
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- by Robert Ghrist PDF
- Bull. Amer. Math. Soc. 45 (2008), 61-75
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.References
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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.
- © Copyright 2007 Robert W. 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
- MathSciNet review: 2358377