• Corpus ID: 238634284

# Reeb Graph Metrics from the Ground Up

@article{Bollen2021ReebGM,
title={Reeb Graph Metrics from the Ground Up},
author={Brian Bollen and Erin W. Chambers and Joshua A. Levine and E. Munch},
journal={ArXiv},
year={2021},
volume={abs/2110.05631}
}
• Published 11 October 2021
• Computer Science
• ArXiv
The Reeb graph has been utilized in various applications including the analysis of scalar fields. Recently, research has been focused on using topological signatures such as the Reeb graph to compare multiple scalar fields by defining distance metrics on the topological signatures themselves. Here we survey five existing metrics that have been defined on Reeb graphs: the bottleneck distance, the interleaving distance, functional distortion distance, the Reeb graph edit distance, and the…
3 Citations
Intrinsic Interleaving Distance for Merge Trees
• Computer Science
ArXiv
• 2019
It is shown that the interleaving distance is intrinsic on the space of labeled merge trees and provided an algorithm to construct metric 1-centers for collections of labeling merge trees, and it is proved that the intrinsic property of the Interleaving Distance also holds for thespace of unlabeled merge trees.
Adaptive Covers for Mapper Graphs Using Information Criteria
• Computer Science, Mathematics
2021 IEEE International Conference on Big Data (Big Data)
• 2021
This work explores how information criteria used in the X-means clustering algorithm can inform and generate adaptive covers for mapper graphs and makes novel progress towards automatic parameter selection for the mapper construction using information theory.
The Universal $\ell^p$-Metric on Merge Trees
• Computer Science
• 2021
An `-type extension of the interleaving distance on merge trees is introduced, and it is proved that this distance is stable with respect to cellular sublevel filtrations and that it is the universal (i.e., largest) distance satisfying this stability property.

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