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arXiv · 1912.02563

Universality of persistence diagrams and the bottleneck and Wasserstein distances

Peter Bubenik·Alex Elchesen
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Abstract

We prove that persistence diagrams with the p-Wasserstein distance form the universal p-subadditive commutative monoid on an underlying metric space with a distinguished subset. This result applies to persistence diagrams, barcodes, and to multiparameter persistence modules. In addition, the 1-Wasserstein distance satisfies Kantorovich-Rubinstein duality.

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Peter Bubenik, Alex Elchesen. 2019-12-05. Universality of persistence diagrams and the bottleneck and Wasserstein distances. https://doi.org/10.1016/j.comgeo.2022.101882

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