Emergent Mind
Nonembeddability of Persistence Diagrams with $p>2$ Wasserstein Metric
(1910.13935)
Published Oct 30, 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.
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