Nonembeddability of Persistence Diagrams with p>2 Wasserstein Metric

10/30/2019
by   Alexander Wagner, et al.
0

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.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset