Stability of persistence diagrams

D. Cohen Steiner, H. Edelsbrunner, J. Harer, Discrete & Computational Geometry 37 (2007) 103–120.

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Abstract
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.
Publishing Year
Date Published
2007-01-01
Journal Title
Discrete & Computational Geometry
Volume
37
Issue
1
Page
103 - 120
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Cohen Steiner D, Edelsbrunner H, Harer J. Stability of persistence diagrams. Discrete & Computational Geometry. 2007;37(1):103-120. doi:10.1007/s00454-006-1276-5
Cohen Steiner, D., Edelsbrunner, H., & Harer, J. (2007). Stability of persistence diagrams. Discrete & Computational Geometry, 37(1), 103–120. https://doi.org/10.1007/s00454-006-1276-5
Cohen Steiner, David, Herbert Edelsbrunner, and John Harer. “Stability of Persistence Diagrams.” Discrete & Computational Geometry 37, no. 1 (2007): 103–20. https://doi.org/10.1007/s00454-006-1276-5.
D. Cohen Steiner, H. Edelsbrunner, and J. Harer, “Stability of persistence diagrams,” Discrete & Computational Geometry, vol. 37, no. 1, pp. 103–120, 2007.
Cohen Steiner D, Edelsbrunner H, Harer J. 2007. Stability of persistence diagrams. Discrete & Computational Geometry. 37(1), 103–120.
Cohen Steiner, David, et al. “Stability of Persistence Diagrams.” Discrete & Computational Geometry, vol. 37, no. 1, Springer, 2007, pp. 103–20, doi:10.1007/s00454-006-1276-5.

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