Nonembeddability of Persistence Diagrams with $p>2$ Wasserstein Metric

Alexander Wagner

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arXiv · 1910.13935

Nonembeddability of Persistence Diagrams with $p>2$ Wasserstein Metric

Alexander Wagner

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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 persistence diagrams with the p-Wasserstein metric do not admit a coarse embedding into a Hilbert space when p > 2.

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Alexander Wagner. 2019-10-30. Nonembeddability of Persistence Diagrams with $p>2$ Wasserstein Metric. https://arxiv.org/abs/1910.13935

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