Nonembeddability of persistence diagrams with 𝑝>2 Wasserstein metric

Wagner, Alexander

doi:10.1090/proc/15451

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 $p > 2$.

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