Visualizing Multivariate Data Using Singularity Theory

  • Osamu Saeki
  • Shigeo Takahashi
  • Daisuke Sakurai
  • Hsiang-Yun Wu
  • Keisuke  Kikuchi
  • Hamish Carr
  • David Duke
  • Takahiro Yamamoto
Conference paper
Part of the Mathematics for Industry book series (MFI, volume 1)

Abstract

This is a survey article on recent developments in visualization of large data, especially that of multivariate volume data. We present two essential ingredients. The first one is the mathematical background, especially the singularity theory of differentiable mappings, which enables us to capture topological features of given multivariate data in a mathematically rigorous way. The second one is a new development in computer science, called the joint contour net, which can encode topological structures of a given set of multivariate data in an efficient and robust way. Some applications to real data analysis are also presented.

Keywords

Multivariate data Singular fiber Differential topology Joint contour net Reeb space Data visualization Jacobi set 3-Manifold with boundary 

Notes

Acknowledgments

The “Hurricane Isabel” data set was produced by the Weather Research and Forecast (WRF) model, courtesy of NCAR and the U.S. National Science Foundation (NSF). This research has been partially supported by JSPS KAKENHI Grant Number 25540041, and EPSRC EP/J013072/1.

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Copyright information

© Springer Japan 2014

Authors and Affiliations

  • Osamu Saeki
    • 1
  • Shigeo Takahashi
    • 2
  • Daisuke Sakurai
    • 2
  • Hsiang-Yun Wu
    • 2
  • Keisuke  Kikuchi
    • 2
  • Hamish Carr
    • 3
  • David Duke
    • 3
  • Takahiro Yamamoto
    • 4
  1. 1.Institute of Mathematics for IndustryKyushu UniversityNishi-kuJapan
  2. 2.Graduate School of Frontier SciencesThe University of TokyoKashiwaJapan
  3. 3.School of ComputingUniversity of LeedsLeedsUK
  4. 4.Faculty of EngineeringKyushu Sangyo UniversityFukuokaJapan

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