Stability of persistence diagrams
Publication
, Journal Article
Cohen-Steiner, D; Edelsbrunner, H; Harer, J
Published in: Discrete and Computational Geometry
January 1, 2007
The persistence diagram of a real-valued function on a topological space is a multiset of points in the extended plane. We prove that under mild assumptions on the function, the persistence diagram is stable: small changes in the function imply only small changes in the diagram. We apply this result to estimating the homology of sets in a metric space and to comparing and classifying geometric shapes. © 2006 Springer.
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Published In
Discrete and Computational Geometry
DOI
EISSN
1432-0444
ISSN
0179-5376
Publication Date
January 1, 2007
Volume
37
Issue
1
Start / End Page
103 / 120
Related Subject Headings
- Computation Theory & Mathematics
- 49 Mathematical sciences
- 46 Information and computing sciences
- 0802 Computation Theory and Mathematics
- 0103 Numerical and Computational Mathematics
- 0101 Pure Mathematics
Citation
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ICMJE
MLA
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Cohen-Steiner, D., Edelsbrunner, H., & Harer, J. (2007). Stability of persistence diagrams. Discrete and Computational Geometry, 37(1), 103–120. https://doi.org/10.1007/s00454-006-1276-5
Cohen-Steiner, D., H. Edelsbrunner, and J. Harer. “Stability of persistence diagrams.” Discrete and Computational Geometry 37, no. 1 (January 1, 2007): 103–20. https://doi.org/10.1007/s00454-006-1276-5.
Cohen-Steiner D, Edelsbrunner H, Harer J. Stability of persistence diagrams. Discrete and Computational Geometry. 2007 Jan 1;37(1):103–20.
Cohen-Steiner, D., et al. “Stability of persistence diagrams.” Discrete and Computational Geometry, vol. 37, no. 1, Jan. 2007, pp. 103–20. Scopus, doi:10.1007/s00454-006-1276-5.
Cohen-Steiner D, Edelsbrunner H, Harer J. Stability of persistence diagrams. Discrete and Computational Geometry. 2007 Jan 1;37(1):103–120.
Published In
Discrete and Computational Geometry
DOI
EISSN
1432-0444
ISSN
0179-5376
Publication Date
January 1, 2007
Volume
37
Issue
1
Start / End Page
103 / 120
Related Subject Headings
- Computation Theory & Mathematics
- 49 Mathematical sciences
- 46 Information and computing sciences
- 0802 Computation Theory and Mathematics
- 0103 Numerical and Computational Mathematics
- 0101 Pure Mathematics