Bottleneck stability for generalized persistence diagrams
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- by Alex McCleary and Amit Patel PDF
- Proc. Amer. Math. Soc. 148 (2020), 3149-3161 Request permission
Abstract:
In this paper, we extend bottleneck stability to the setting of one dimensional constructible persistence modules valued in any skeletally small abelian category.References
- Peter Bubenik, Vin de Silva, and Vidit Nanda, Higher interpolation and extension for persistence modules, SIAM J. Appl. Algebra Geom. 1 (2017), no. 1, 272–284. MR 3683688, DOI 10.1137/16M1100472
- Gunnar Carlsson and Vin de Silva, Zigzag persistence, Found. Comput. Math. 10 (2010), no. 4, 367–405. MR 2657946, DOI 10.1007/s10208-010-9066-0
- Frédéric Chazal, David Cohen-Steiner, Marc Glisse, Leonidas Guibas, and Steve Oudot, Proximity of persistence modules and their diagrams, Proceedings of the twenty-fifth annual symposium on computational geometry, 2009, pp. 237–246.
- Frédéric Chazal, Vin de Silva, Marc Glisse, and Steve Oudot, The structure and stability of persistence modules, SpringerBriefs in Mathematics, Springer, [Cham], 2016. MR 3524869, DOI 10.1007/978-3-319-42545-0
- David Cohen-Steiner, Herbert Edelsbrunner, and John Harer, Stability of persistence diagrams, Discrete & Computational Geometry 37 (2007), no. 1, 103–120 (English)., DOI 10.1007/s00454-006-1276-5
- William Crawley-Boevey, Decomposition of pointwise finite-dimensional persistence modules, J. Algebra Appl. 14 (2015), no. 5, 1550066, 8. MR 3323327, DOI 10.1142/S0219498815500668
- Amit Patel, Generalized persistence diagrams, J. Appl. Comput. Topol. 1 (2018), no. 3-4, 397–419. MR 3975559, DOI 10.1007/s41468-018-0012-6
- Afra Zomorodian and Gunnar Carlsson, Computing persistent homology, Discrete & Computational Geometry 33 (2005), no. 2, 249–274 (English)., DOI 10.1007/s00454-004-1146-y
Additional Information
- Alex McCleary
- Affiliation: Department of Mathematics, Colorado State University, Fort Collins, Colorado 80523
- MR Author ID: 1301682
- Amit Patel
- Affiliation: Department of Mathematics, Colorado State University, Fort Collins, Colorado 80523
- MR Author ID: 871669
- Received by editor(s): July 6, 2018
- Received by editor(s) in revised form: April 6, 2019, July 30, 2019, and November 2, 2019
- Published electronically: March 30, 2020
- Additional Notes: This research was partially supported by NSF grant CCF 1717159
- Communicated by: Mark Behrens
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 3149-3161
- MSC (2010): Primary 55U99; Secondary 55N99, 05E99
- DOI: https://doi.org/10.1090/proc/14929
- MathSciNet review: 4099800