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The mergegram of a dendrogram and its stability

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arxiv 2007.11278 v1 pith:ZAVYVKTI submitted 2020-07-22 cs.CG

The mergegram of a dendrogram and its stability

classification cs.CG
keywords persistencecloudsdatadendrogrammergegrampointstopologicalanalysis
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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.

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