---
_id: '3972'
abstract:
- lang: eng
text: '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.'
author:
- first_name: David
full_name: Cohen-Steiner, David
last_name: Cohen Steiner
- first_name: Herbert
full_name: Herbert Edelsbrunner
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: John
full_name: Harer, John
last_name: Harer
citation:
ama: 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
apa: Cohen Steiner, D., Edelsbrunner, H., & Harer, J. (2007). Stability of persistence
diagrams. Discrete & Computational Geometry. Springer. https://doi.org/10.1007/s00454-006-1276-5
chicago: Cohen Steiner, David, Herbert Edelsbrunner, and John Harer. “Stability
of Persistence Diagrams.” Discrete & Computational Geometry. Springer,
2007. https://doi.org/10.1007/s00454-006-1276-5.
ieee: D. Cohen Steiner, H. Edelsbrunner, and J. Harer, “Stability of persistence
diagrams,” Discrete & Computational Geometry, vol. 37, no. 1. Springer,
pp. 103–120, 2007.
ista: Cohen Steiner D, Edelsbrunner H, Harer J. 2007. Stability of persistence diagrams.
Discrete & Computational Geometry. 37(1), 103–120.
mla: 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.
short: D. Cohen Steiner, H. Edelsbrunner, J. Harer, Discrete & Computational
Geometry 37 (2007) 103–120.
date_created: 2018-12-11T12:06:12Z
date_published: 2007-01-01T00:00:00Z
date_updated: 2021-01-12T07:53:34Z
day: '01'
doi: 10.1007/s00454-006-1276-5
extern: 1
intvolume: ' 37'
issue: '1'
month: '01'
page: 103 - 120
publication: Discrete & Computational Geometry
publication_status: published
publisher: Springer
publist_id: '2153'
quality_controlled: 0
status: public
title: Stability of persistence diagrams
type: journal_article
volume: 37
year: '2007'
...