A Finitely Stable Edit Distance for Merge Trees
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866929599260131328 |
|---|---|
| author | Pegoraro, Matteo |
| author_facet | Pegoraro, Matteo |
| contents | In this paper we define a novel edit distance for merge trees, which we argue to be suitable for a good range of applications. Relying also on some technical results contained in other works, we investigate its stability properties, which end up being analogous to the ones of the 1-Wasserstein distance between persistence diagrams. In the appendix, we extensively compare our metric in relationship with other metrics appearing in the literature, with both theoretic and practical considerations and a simulation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_02738 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A Finitely Stable Edit Distance for Merge Trees Pegoraro, Matteo Metric Geometry General Topology In this paper we define a novel edit distance for merge trees, which we argue to be suitable for a good range of applications. Relying also on some technical results contained in other works, we investigate its stability properties, which end up being analogous to the ones of the 1-Wasserstein distance between persistence diagrams. In the appendix, we extensively compare our metric in relationship with other metrics appearing in the literature, with both theoretic and practical considerations and a simulation. |
| title | A Finitely Stable Edit Distance for Merge Trees |
| topic | Metric Geometry General Topology |
| url | https://arxiv.org/abs/2111.02738 |