Advertisement

Dimension Reduction Based on Geometric Reasoning for Reducts

  • Naohiro Ishii
  • Ippei Torii
  • Kazunori Iwata
  • Kazuya Odagiri
  • Toyoshiro Nakashima
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 840)

Abstract

Dimension reduction of data is an important problem and it is needed for the analysis of higher dimensional data in the application domain. Rough set is fundamental and useful to reduce higher dimensional data to lower one for the classification. We develop generation of reducts based on nearest neighbor relation for the classification. In this paper, the nearest neighbor relation is shown to play a fundamental role for the classification from the geometric reasoning. First, the nearest neighbor relation is characterized by the complexity order. Next, it is shown that reducts are characterized and generated based on the nearest neighbor relations based on the degenerate convex cones. Finally, the algebraic operations on the degenerate convex cones are developed for the generation of reducts.

Keywords

Reduct Nearest neighbor relation Characterization of reducts Convex cones Degenerate convex cones 

References

  1. 1.
    Pawlak, Z.: Rough sets. Int. J. Comput. Inf. Sci. 11, 341–356 (1982)CrossRefGoogle Scholar
  2. 2.
    Skowron, A., Rauszer, C.: The discernibility matrices and functions in information systems. In: Intelligent Decision Support - Handbook of Application and Advances of Rough Sets Theory, pp. 331–362. Kluwer Academic Publishers, Dordrecht (1992)Google Scholar
  3. 3.
    Skowron, A., Polkowski, L.: Decision algorithms, a survey of rough set theoretic methods. Fundamenta Informatica 30(3–4), 345–358 (1997)MathSciNetMATHGoogle Scholar
  4. 4.
    Cover, T.M., Hart, P.E.: Nearest neighbor pattern classification. IEEE Trans. Inf. Theor. 13(1), 21–27 (1967)CrossRefGoogle Scholar
  5. 5.
    Preparata, F.P., Shamos, M.I.: Computational Geometry. Springer (1993)Google Scholar
  6. 6.
    Prenowitz, W., Jantosciak, J.: Join Geometries, A Theory of Convex Sets and Linear Geometry. Springer (2013)Google Scholar
  7. 7.
    Levitin, A.: Introduction to the Design & Analysis of Algorithms, 3rd edn. Person Publication (2012)Google Scholar
  8. 8.
    Ishii, N., Torii, I., Mukai, N., Iwata, K., Nakashima, T.: Classification on nonlinear mapping of reducts based on nearest neighbor relation. In: Proceedings ACIS-ICIS IEEE Computer Society, pp. 491–496 (2015)Google Scholar
  9. 9.
    Ishii, N., Torii, I., Iwata, K., Nakashima, T.: Generation and nonlinear mapping of reducts-nearest neighbor classification. In: Advances in Combining Intelligent Methods, pp. 93–108. Springer (2017). Chapter 5Google Scholar
  10. 10.
    Ishii, N., Torii, I., Iwata, K., Odagiri, K., Nakashima, T.: Generation of reducts based on nearest neighbor relations and boolean reasoning. In: HAIS2017, LNCS, vol. 10334, pp. 391–401. Springer (2017)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Naohiro Ishii
    • 1
  • Ippei Torii
    • 1
  • Kazunori Iwata
    • 2
  • Kazuya Odagiri
    • 3
  • Toyoshiro Nakashima
    • 3
  1. 1.Aichi Institute of TechnologyToyotaJapan
  2. 2.Aichi UniversityNagoyaJapan
  3. 3.Sugiyama Jyogakuen UniversityNagoyaJapan

Personalised recommendations