--- _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' ...