License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2022.24
URN: urn:nbn:de:0030-drops-160325
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16032/
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Cardona, Robert ; Curry, Justin ; Lam, Tung ; Lesnick, Michael

The Universal ?^p-Metric on Merge Trees

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LIPIcs-SoCG-2022-24.pdf (0.8 MB)

Abstract

Adapting a definition given by Bjerkevik and Lesnick for multiparameter persistence modules, we introduce an ?^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 ∈ [1,∞], 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 = ∞ 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 ?^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
Collection: 38th International Symposium on Computational Geometry (SoCG 2022)
Issue Date: 2022
Date of publication: 01.06.2022

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