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Measuring the Distance Between Merge Trees

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Topological Methods in Data Analysis and Visualization III

Part of the book series: Mathematics and Visualization ((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).

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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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Authors and Affiliations

  1. Lawrence Berkeley National Laboratory, One Cyclotron Rd, Berkeley, CA, 94720, USA

    Kenes Beketayev, Dmitriy Morozov & Gunther H. Weber

  2. Nazarbayev University, 53 Kabanbay Batyr Ave, Astana, 010000, Kazakhstan

    Kenes Beketayev

  3. Kazakh-British Technical University, 59 Tole Bi St, Almaty, 050000, Kazakhstan

    Damir Yeliussizov

  4. Department of Computer Science, Institute for Data Analysis and Visualization (IDAV), University of California, Davis, CA, 95616-8562, USA

    Gunther H. Weber & Bernd Hamann

Authors
  1. Kenes Beketayev
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  2. Damir Yeliussizov
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  3. Dmitriy Morozov
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  4. Gunther H. Weber
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  5. Bernd Hamann
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Corresponding author

Correspondence to Kenes Beketayev .

Editor information

Editors and Affiliations

  1. Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, Livermore, California, USA

    Peer-Timo Bremer

  2. Comparative Visualization Group, Konrad-Zuse-Zentrum für Informationstechnik, Berlin, Germany

    Ingrid Hotz

  3. School of Computing and SCI Institute, University of Utah, Salt Lake City, Utah, USA

    Valerio Pascucci

  4. Department of Computer Science, ETH Zürich, Zürich, Switzerland

    Ronald Peikert

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© 2014 Springer International Publishing Switzerland

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Beketayev, K., Yeliussizov, D., Morozov, D., Weber, G.H., Hamann, B. (2014). Measuring the Distance Between Merge Trees. In: Bremer, PT., Hotz, I., Pascucci, V., Peikert, R. (eds) Topological Methods in Data Analysis and Visualization III. Mathematics and Visualization. Springer, Cham. https://doi.org/10.1007/978-3-319-04099-8_10

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