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)


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.


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


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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

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