About the Metric Space of Merge Trees with the Edit Distance
M. Pegoraro · arXiv (Cornell University) · 2021
In this paper we consider the metric space of of merge trees endued with an edit distance and we start to study the properties of such space. This investigation is intended as a first step into a geometric understanding of this space, aiming at defining exploratory tools and statistical tools. In particular, we present some results about its topological properties and its geodesic structure, with particular attention to objects called Frech\`et Means.