Elkin, Yury and Kurlin, Vitaliy 
ORCID: 0000-0001-5328-5351
(2020)
The mergegram of a dendrogram and its stability.
In: Mathematical Foundations of Computer Science.
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Abstract
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.
| Item Type: | Conference or Workshop Item (Unspecified) |
|---|---|
| Uncontrolled Keywords: | cs.CG, cs.CG |
| Depositing User: | Symplectic Admin |
| Date Deposited: | 30 Jul 2020 13:49 |
| Last Modified: | 18 Jan 2023 23:39 |
| DOI: | 10.4230/LIPIcs.MFCS.2020.32 |
| Related URLs: | |
| URI: | https://livrepository.liverpool.ac.uk/id/eprint/3095223 |
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