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arXiv · 2111.02738

A Finitely Stable Edit Distance for Merge Trees

Matteo Pegoraro
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Abstract

In this paper we define a novel edit distance for merge trees, which we argue to be suitable for a good range of applications. Relying also on some technical results contained in other works, we investigate its stability properties, which end up being analogous to the ones of the 1-Wasserstein distance between persistence diagrams. In the appendix, we extensively compare our metric in relationship with other metrics appearing in the literature, with both theoretic and practical considerations and a simulation.

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Matteo Pegoraro. 2021-11-04. A Finitely Stable Edit Distance for Merge Trees. https://arxiv.org/abs/2111.02738

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