2026-07-23T12:54:48Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:12728 2024-03-06T10:50:37Z ddc:004 open_access

The Mergegram of a Dendrogram and Its Stability Elkin, Yury Kurlin, Vitaliy clustering dendrogram topological data analysis persistence stability This paper extends the key concept of persistence within Topological Data Analysis (TDA) in a new direction. TDA quantifies topological shapes hidden in unorganized data such as clouds of unordered points. In the 0-dimensional case the distance-based persistence is determined by a single-linkage (SL) clustering of a finite set in a metric space. Equivalently, the 0D persistence captures only edge-lengths of a Minimum Spanning Tree (MST). Both SL dendrogram and MST are unstable under perturbations of points. We define the new stable-under-noise mergegram, which outperforms previous isometry invariants on a classification of point clouds by PersLay. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Yury Elkin and Vitaliy Kurlin 2020 Is Part Of LIPIcs, Volume 170, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.MFCS.2020.32 urn:nbn:de:0030-drops-127281 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.32 eng https://creativecommons.org/licenses/by/3.0/legalcode