Stability of Persistence Diagrams

Stability of Persistence Diagrams. Cohen-Steiner, D., Edelsbrunner, H., & Harer, J. 37(1):103-120.

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.

@article{cohen-steinerStabilityPersistenceDiagrams2007,
  langid = {english},
  title = {Stability of {{Persistence Diagrams}}},
  volume = {37},
  issn = {0179-5376, 1432-0444},
  url = {https://link.springer.com/article/10.1007/s00454-006-1276-5},
  doi = {10.1007/s00454-006-1276-5},
  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.},
  number = {1},
  journaltitle = {Discrete \& Computational Geometry},
  shortjournal = {Discrete Comput Geom},
  urldate = {2018-07-31},
  date = {2007-01-01},
  pages = {103-120},
  author = {Cohen-Steiner, David and Edelsbrunner, Herbert and Harer, John},
  file = {/home/dimitri/Nextcloud/Zotero/storage/4WEUZ4B5/Cohen-Steiner et al. - 2007 - Stability of Persistence Diagrams.pdf;/home/dimitri/Nextcloud/Zotero/storage/5P323WWZ/s00454-006-1276-5.html}
}

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