2000 character limit reached
Nonembeddability of Persistence Diagrams with $p>2$ Wasserstein Metric (1910.13935v1)
Published 30 Oct 2019 in math.FA, cs.LG, math.AT, and math.MG
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.
Sponsor
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.