Nonembeddability of persistence diagrams with $p>2$ Wasserstein metric
Copyright policy )Nonembeddability of persistence diagrams with $p>2$ Wasserstein metric
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.
- Duke University United States
- University of Florida United States
FOS: Computer and information sciences, Computer Science - Machine Learning, Metric Geometry (math.MG), Persistent homology and applications, topological data analysis, Functional Analysis (math.FA), Machine Learning (cs.LG), Mathematics - Functional Analysis, Mathematics - Metric Geometry, Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product), FOS: Mathematics, Algebraic Topology (math.AT), Mathematics - Algebraic Topology, 55N99, 46C05
FOS: Computer and information sciences, Computer Science - Machine Learning, Metric Geometry (math.MG), Persistent homology and applications, topological data analysis, Functional Analysis (math.FA), Machine Learning (cs.LG), Mathematics - Functional Analysis, Mathematics - Metric Geometry, Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product), FOS: Mathematics, Algebraic Topology (math.AT), Mathematics - Algebraic Topology, 55N99, 46C05
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