Nonembeddability of persistence diagrams with ๐>2 Wasserstein metric
Alexander Wagner ยท Proceedings of the American Mathematical Society ยท 2021
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 p -Wasserstein metric do not admit a coarse embedding into a Hilbert space when p > 2 p > 2 .