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Measuring the Distance Between Merge Trees

  • Kenes Beketayev
  • Damir Yeliussizov
  • Dmitriy Morozov
  • Gunther H. Weber
  • Bernd Hamann
Conference paper
Part of the Mathematics and Visualization book series (MATHVISUAL)

Abstract

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).

Keywords

Edit Distance Root Branch Naive Algorithm Reeb Graph Persistent Homology 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

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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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Kenes Beketayev
    • 1
    • 2
  • Damir Yeliussizov
    • 3
  • Dmitriy Morozov
    • 1
  • Gunther H. Weber
    • 1
    • 4
  • Bernd Hamann
    • 4
  1. 1.Lawrence Berkeley National LaboratoryBerkeleyUSA
  2. 2.Nazarbayev UniversityAstanaKazakhstan
  3. 3.Kazakh-British Technical UniversityAlmatyKazakhstan
  4. 4.Department of Computer Science, Institute for Data Analysis and Visualization (IDAV)University of CaliforniaDavisUSA

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