Nonembeddability of Persistence Diagrams with $p>2$ Wasserstein Metric
Functional Analysis
2019-10-31 v1 Machine Learning
Algebraic Topology
Metric Geometry
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.
Keywords
Cite
@article{arxiv.1910.13935,
title = {Nonembeddability of Persistence Diagrams with $p>2$ Wasserstein Metric},
author = {Alexander Wagner},
journal= {arXiv preprint arXiv:1910.13935},
year = {2019}
}