Nonembeddability of persistence diagrams with $p>2$ Wasserstein metric
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- by Alexander Wagner
- Proc. Amer. Math. Soc. 149 (2021), 2673-2677
- DOI: https://doi.org/10.1090/proc/15451
- Published electronically: March 29, 2021
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Abstract:
Persistence diagrams do not admit an inner product structure compatible with any Wasserstein metric. Hence, when applying kernel methods to persistence diagrams, the underlying feature map necessarily causes distortion. We prove that persistence diagrams with the $p$-Wasserstein metric do not admit a coarse embedding into a Hilbert space when $p > 2$.References
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Bibliographic Information
- Alexander Wagner
- Affiliation: Department of Mathematics, University of Florida, Gainesville, Florida 32601
- Address at time of publication: Department of Mathematics, Duke University, Durham, North Carolina 27708
- MR Author ID: 1382251
- ORCID: 0000-0002-5961-7852
- Email: alexander.wagner@duke.edu
- Received by editor(s): February 18, 2020
- Published electronically: March 29, 2021
- Communicated by: Deane Yang
- © Copyright 2021 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 149 (2021), 2673-2677
- MSC (2020): Primary 55N99, 46C05
- DOI: https://doi.org/10.1090/proc/15451
- MathSciNet review: 4246816