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A Comparison of Pareto Sets and Jacobi Sets

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Topological and Statistical Methods for Complex Data

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

Abstract

Topological analysis of multifields is an approaches to find meaningful, intrinsic structures in complex data. Methods introduced in previous years were usually evaluated separately or rather informally. However, to aid the decision which method is best suited for a particular kind of data, it is important to compare and put them into context with each other. Using results from optimization mathematics, this paper finds subset and equivalence relations between Jacobi Sets and Pareto Sets and indicates even further relations to Morse decomposition. This is a first step towards the creation of new analysis tools for multifield topology and of new insight about how the topological approaches are connected with each other.

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Author information

Authors and Affiliations

  1. University of Kaiserslautern, Kaiserslautern, Germany

    Lars Huettenberger & Christoph Garth

Authors
  1. Lars Huettenberger
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  2. Christoph Garth
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Corresponding author

Correspondence to Christoph Garth .

Editor information

Editors and Affiliations

  1. Sandia National Laboratories, MS 9152, Livermore, California, USA

    Janine Bennett

  2. CEA CESTA, CS 60001, Le Barp CEDEX, France

    Fabien Vivodtzev

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

    Valerio Pascucci

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Huettenberger, L., Garth, C. (2015). A Comparison of Pareto Sets and Jacobi Sets. In: Bennett, J., Vivodtzev, F., Pascucci, V. (eds) Topological and Statistical Methods for Complex Data. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44900-4_8

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