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Nonembeddability of persistence diagrams with $p>2$ Wasserstein metric


Author: Alexander Wagner
Journal: Proc. Amer. Math. Soc. 149 (2021), 2673-2677
MSC (2020): Primary 55N99, 46C05
DOI: https://doi.org/10.1090/proc/15451
Published electronically: March 29, 2021
MathSciNet review: 4246816
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Abstract | References | Similar Articles | Additional Information

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 $p > 2$.


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Additional 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
Article copyright: © Copyright 2021 American Mathematical Society