A Metric for Tree-Like Topological Summaries
Year: 2021
Type: preprint
Abstract: In this work we define a novel metric structure for a family of tree-like topological summaries. This family of objects is a natural combinatoric generalization of merge trees of scalar fields and hierarchical dendrograms. The metric introduced can be computed with a dynamical integer linear programming approach and we showcase its feasibility and the effectiveness of the whole framework with simulated data sets. In particular we stress the versatility of these topological summaries, which prove to be very effective in situation where other topological data analysis tools, like persistence diagrams, can not be meaningfully employed.
Source: arXiv (Cornell University)
Author: M. Pegoraro
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3197744483