Edit Distance and Persistence Diagrams Over Lattices
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866913482177249280 |
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| author | McCleary, Alexander Patel, Amit |
| author_facet | McCleary, Alexander Patel, Amit |
| contents | We build a functorial pipeline for persistent homology. The input to this pipeline is a filtered simplicial complex indexed by any finite metric lattice and the output is a persistence diagram defined as the Möbius inversion of its birth-death function. We adapt the Reeb graph edit distance to each of our categories and prove that both functors in our pipeline are $1$-Lipschitz making our pipeline stable. Our constructions generalize the classical persistence diagram and, in this setting, the bottleneck distance is strongly equivalent to the edit distance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_07337 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Edit Distance and Persistence Diagrams Over Lattices McCleary, Alexander Patel, Amit Algebraic Topology Computational Geometry We build a functorial pipeline for persistent homology. The input to this pipeline is a filtered simplicial complex indexed by any finite metric lattice and the output is a persistence diagram defined as the Möbius inversion of its birth-death function. We adapt the Reeb graph edit distance to each of our categories and prove that both functors in our pipeline are $1$-Lipschitz making our pipeline stable. Our constructions generalize the classical persistence diagram and, in this setting, the bottleneck distance is strongly equivalent to the edit distance. |
| title | Edit Distance and Persistence Diagrams Over Lattices |
| topic | Algebraic Topology Computational Geometry |
| url | https://arxiv.org/abs/2010.07337 |