Measuring the Distance Between Merge Trees
Merge trees represent the topology of scalar functions. To assess the topological similarity of functions, one can compare their merge trees. To do so, one needs a notion of a distance between merge trees, which we define. We provide examples of using our merge tree distance and compare this new measure to other ways used to characterize topological similarity (bottleneck distance for persistence diagrams) and numerical difference (L ∞ -norm of the difference between functions).
KeywordsEdit Distance Root Branch Naive Algorithm Reeb Graph Persistent Homology
The authors thank Aidos Abzhanov. This work was supported by the Director, Office of Advanced Scientific Computing Research, Office of Science, of the U.S. DOE under Contract No. DE-AC02-05CH11231 (Berkeley Lab), and the Program 055 of the Ministry of Edu. and Sci. of the Rep. of Kazakhstan under the contract with the CER, Nazarbayev University.
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