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DOI: 10.4230/LIPIcs.SoCG.2022.24
URN: urn:nbn:de:0030-drops-160325
URL: https://drops.dagstuhl.de/opus/volltexte/2022/16032/
Cardona, Robert ; Curry, Justin ; Lam, Tung ; Lesnick, Michael
The Universal π^p-Metric on Merge Trees
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Abstract
Adapting a definition given by Bjerkevik and Lesnick for multiparameter persistence modules, we introduce an π^p-type extension of the interleaving distance on merge trees. We show that our distance is a metric, and that it upper-bounds the p-Wasserstein distance between the associated barcodes. For each p β [1,β], we prove that this distance is stable with respect to cellular sublevel filtrations and that it is the universal (i.e., largest) distance satisfying this stability property. In the p = β case, this gives a novel proof of universality for the interleaving distance on merge trees.
BibTeX - Entry
@InProceedings{cardona_et_al:LIPIcs.SoCG.2022.24,
author = {Cardona, Robert and Curry, Justin and Lam, Tung and Lesnick, Michael},
title = {{The Universal π^p-Metric on Merge Trees}},
booktitle = {38th International Symposium on Computational Geometry (SoCG 2022)},
pages = {24:1--24:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-227-3},
ISSN = {1868-8969},
year = {2022},
volume = {224},
editor = {Goaoc, Xavier and Kerber, Michael},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2022/16032},
URN = {urn:nbn:de:0030-drops-160325},
doi = {10.4230/LIPIcs.SoCG.2022.24},
annote = {Keywords: merge trees, hierarchical clustering, persistent homology, Wasserstein distances, interleavings}
}
| Keywords: | merge trees, hierarchical clustering, persistent homology, Wasserstein distances, interleavings | |
| Seminar: | 38th International Symposium on Computational Geometry (SoCG 2022) | |
| Issue date: | 2022 | |
| Date of publication: | 01.06.2022 |
