Universality of persistence diagrams and the bottleneck and Wasserstein distances
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2019
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| _version_ | 1866915155743342592 |
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| author | Bubenik, Peter Elchesen, Alex |
| author_facet | Bubenik, Peter Elchesen, Alex |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1912_02563 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Universality of persistence diagrams and the bottleneck and Wasserstein distances Bubenik, Peter Elchesen, Alex Algebraic Topology Computational Geometry 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. |
| title | Universality of persistence diagrams and the bottleneck and Wasserstein distances |
| topic | Algebraic Topology Computational Geometry |
| url | https://arxiv.org/abs/1912.02563 |