Universality of persistence diagrams and the bottleneck and Wasserstein distances

Abstract

We prove that persistence diagrams with the p-Wasserstein distance form the universal p-subadditive commutative monoid on an underlying metric space with a distinguished subset. This result applies to persistence diagrams, barcodes, and to multiparameter persistence modules. In addition, the 1-Wasserstein distance satisfies Kantorovich-Rubinstein duality.

arXiv comment24 pages, v4: Made changes suggested by the referees

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• Metrics for generalized persistence modules
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• Algebraic Stability of Zigzag Persistence Modules
• Stability of higher-dimensional interval decomposable persistence modules
• Wasserstein Stability for Persistence Diagrams
• Virtual persistence diagrams, signed measures, Wasserstein distances, and Banach spaces
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• Universality of persistence diagrams and the bottleneck and Wasserstein distances
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Cited by in corpus (6)

• Virtual persistence diagrams, signed measures, Wasserstein distances, and Banach spaces
• Universality of persistence diagrams and the bottleneck and Wasserstein distances
• Exact weights, path metrics, and algebraic Wasserstein distances
• Basic Metric Geometry of the Bottleneck Distance
• Metric Geometry of Spaces of Persistence Diagrams
• Topological and metric properties of spaces of generalized persistence diagrams