| dc.contributor.author | Matteo Pegoraro | |
| dc.contributor.other | Department of Mathematics, KTH, Stockholm 10044, Sweden | |
| dc.date.accessioned | 2025-08-27T02:32:33Z | |
| dc.date.accessioned | 2025-10-08T08:22:32Z | |
| dc.date.available | 2025-10-08T08:22:32Z | |
| dc.date.issued | 01-07-2025 | |
| dc.identifier.uri | https://www.aimspress.com/article/doi/10.3934/math.2025769 | |
| dc.identifier.uri | http://digilib.fisipol.ugm.ac.id/repo/handle/15717717/35646 | |
| dc.description.abstract | In this paper, we defined a novel edit distance for merge trees, which we argued to be suitable for a broad range of applications. Relying also on some technical results contained in other works, we investigated its stability properties, which ended up being analogous to the ones of the 1-Wasserstein distance between persistence diagrams. We tested and compared our metric against the interleaving distance in several simulations and case studies, highlighting the trade-off between stability and sensitivity when choosing the appropriate metric for a given data analysis problem, much alike the bias-variance trade-off in statistical modeling. In the appendix, we also compared our metric with other edit distances appearing in the literature, with both theoretic and practical considerations. | |
| dc.language.iso | EN | |
| dc.publisher | AIMS Press | |
| dc.subject.lcc | Mathematics | |
| dc.title | A finitely stable edit distance for merge trees | |
| dc.type | Article | |
| dc.description.keywords | topological data analysis | |
| dc.description.keywords | merge trees | |
| dc.description.keywords | interleaving distance | |
| dc.description.keywords | edit distance | |
| dc.description.keywords | binary optimization | |
| dc.description.pages | 17179-17231 | |
| dc.description.doi | 10.3934/math.2025769 | |
| dc.title.journal | AIMS Mathematics | |
| dc.identifier.e-issn | 2473-6988 | |
| dc.identifier.oai | ce97989789444a44b5011611e75196c9 | |
| dc.journal.info | Volume 10, Issue 7 | |
