A Comparison of Pareto Sets and Jacobi Sets View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2015

AUTHORS

Lars Huettenberger , Christoph Garth

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. More... »

PAGES

125-141

References to SciGraph publications

  • 2003-03. Barrier Trees on Poset-Valued Landscapes in GENETIC PROGRAMMING AND EVOLVABLE MACHINES
  • 2010-09-14. Feature Tracking Using Reeb Graphs in TOPOLOGICAL METHODS IN DATA ANALYSIS AND VISUALIZATION
  • 2007. Topology-Based Flow Visualization, The State of the Art in TOPOLOGY-BASED METHODS IN VISUALIZATION
  • Book

    TITLE

    Topological and Statistical Methods for Complex Data

    ISBN

    978-3-662-44899-1
    978-3-662-44900-4

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-662-44900-4_8

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    http://dx.doi.org/10.1007/978-3-662-44900-4_8

    DIMENSIONS

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