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UK Workshop on Computational Intelligence

UKCI 2018: Advances in Computational Intelligence Systems pp 351–361Cite as

Dimension Reduction Based on Geometric Reasoning for Reducts

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Part of the book series: Advances in Intelligent Systems and Computing ((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.

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Author information

Authors and Affiliations

  1. Aichi Institute of Technology, Toyota, Japan

    Naohiro Ishii & Ippei Torii

  2. Aichi University, Nagoya, Japan

    Kazunori Iwata

  3. Sugiyama Jyogakuen University, Nagoya, Japan

    Kazuya Odagiri & Toyoshiro Nakashima

Authors
  1. Naohiro Ishii
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  2. Ippei Torii
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  3. Kazunori Iwata
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  4. Kazuya Odagiri
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  5. Toyoshiro Nakashima
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Corresponding author

Correspondence to Naohiro Ishii .

Editor information

Editors and Affiliations

  1. School of Science and Technology, Nottingham Trent University, Nottingham, United Kingdom

    Ahmad Lotfi

  2. Faculty of Science and Technology, Bournemouth University, Poole, Dorset, United Kingdom

    Hamid Bouchachia

  3. School of Computing, University of Portsmouth, Portsmouth, Hampshire, United Kingdom

    Alexander Gegov

  4. School of Science and Technology, Nottingham Trent University, Nottingham, United Kingdom

    Caroline Langensiepen

  5. College of Science and Technology, Nottingham Trent University, Nottingham, United Kingdom

    Martin McGinnity

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Ishii, N., Torii, I., Iwata, K., Odagiri, K., Nakashima, T. (2019). Dimension Reduction Based on Geometric Reasoning for Reducts. In: Lotfi, A., Bouchachia, H., Gegov, A., Langensiepen, C., McGinnity, M. (eds) Advances in Computational Intelligence Systems. UKCI 2018. Advances in Intelligent Systems and Computing, vol 840. Springer, Cham. https://doi.org/10.1007/978-3-319-97982-3_29

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