The mergegram of a dendrogram and its stability
Computational Geometry
2020-07-23 v1
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.
Keywords
Cite
@article{arxiv.2007.11278,
title = {The mergegram of a dendrogram and its stability},
author = {Yury Elkin and Vitaliy Kurlin},
journal= {arXiv preprint arXiv:2007.11278},
year = {2020}
}