{"abstract":[{"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.","lang":"eng"}],"publication":"Discrete & Computational Geometry","issue":"1","publication_status":"published","title":"Stability of persistence diagrams","quality_controlled":0,"doi":"10.1007/s00454-006-1276-5","author":[{"full_name":"Cohen-Steiner, David","first_name":"David","last_name":"Cohen Steiner"},{"first_name":"Herbert","full_name":"Herbert Edelsbrunner","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Harer","first_name":"John","full_name":"Harer, John"}],"_id":"3972","intvolume":"        37","type":"journal_article","extern":1,"volume":37,"date_updated":"2021-01-12T07:53:34Z","publist_id":"2153","date_published":"2007-01-01T00:00:00Z","day":"01","page":"103 - 120","status":"public","publisher":"Springer","year":"2007","date_created":"2018-12-11T12:06:12Z","month":"01","citation":{"ieee":"D. Cohen Steiner, H. Edelsbrunner, and J. Harer, “Stability of persistence diagrams,” <i>Discrete &#38; Computational Geometry</i>, vol. 37, no. 1. Springer, pp. 103–120, 2007.","mla":"Cohen Steiner, David, et al. “Stability of Persistence Diagrams.” <i>Discrete &#38; Computational Geometry</i>, vol. 37, no. 1, Springer, 2007, pp. 103–20, doi:<a href=\"https://doi.org/10.1007/s00454-006-1276-5\">10.1007/s00454-006-1276-5</a>.","ama":"Cohen Steiner D, Edelsbrunner H, Harer J. Stability of persistence diagrams. <i>Discrete &#38; Computational Geometry</i>. 2007;37(1):103-120. doi:<a href=\"https://doi.org/10.1007/s00454-006-1276-5\">10.1007/s00454-006-1276-5</a>","short":"D. Cohen Steiner, H. Edelsbrunner, J. Harer, Discrete &#38; Computational Geometry 37 (2007) 103–120.","apa":"Cohen Steiner, D., Edelsbrunner, H., &#38; Harer, J. (2007). Stability of persistence diagrams. <i>Discrete &#38; Computational Geometry</i>. Springer. <a href=\"https://doi.org/10.1007/s00454-006-1276-5\">https://doi.org/10.1007/s00454-006-1276-5</a>","ista":"Cohen Steiner D, Edelsbrunner H, Harer J. 2007. Stability of persistence diagrams. Discrete &#38; Computational Geometry. 37(1), 103–120.","chicago":"Cohen Steiner, David, Herbert Edelsbrunner, and John Harer. “Stability of Persistence Diagrams.” <i>Discrete &#38; Computational Geometry</i>. Springer, 2007. <a href=\"https://doi.org/10.1007/s00454-006-1276-5\">https://doi.org/10.1007/s00454-006-1276-5</a>."}}