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The Convex Subclass Method: Combinatorial Classifier Based on a Family of Convex Sets

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Machine Learning and Data Mining in Pattern Recognition (MLDM 2005)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3587))

Abstract

We propose a new nonparametric classification framework for numerical patterns, which can also be exploitable for exploratory data analysis. The key idea is approximating each class region by a family of convex geometric sets which can cover samples of the target class without containing any samples of other classes. According to this framework, we consider a combinatorial classifier based on a family of spheres, each of which is the minimum covering sphere for a subset of positive samples and does not contain any negative samples. We also present a polynomial-time exact algorithm and an incremental randomized algorithm to compute it. In addition, we discuss the soft-classification version and evaluate these algorithms by some numerical experiments.

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Author information

Authors and Affiliations

  1. Bioinformatics Center, Institute for Chemical Research, Kyoto University, Gokasho, Uji, Kyoto, 611-0011, Japan

    Ichigaku Takigawa

  2. Graduate School of Information Science and Technology, Hokkaido University, Kita 13, Nishi 8, Kita-ku, Sapporo, 060-8014, Japan

    Mineichi Kudo & Atsuyoshi Nakamura

Authors
  1. Ichigaku Takigawa
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  2. Mineichi Kudo
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  3. Atsuyoshi Nakamura
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Editor information

Editors and Affiliations

  1. Institute of Computer Vision and applied Computer Sciences, IBaI, Germany

    Petra Perner

  2. Institute of Media and Information Technology, Chiba University, Japan

    Atsushi Imiya

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© 2005 Springer-Verlag Berlin Heidelberg

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Takigawa, I., Kudo, M., Nakamura, A. (2005). The Convex Subclass Method: Combinatorial Classifier Based on a Family of Convex Sets. In: Perner, P., Imiya, A. (eds) Machine Learning and Data Mining in Pattern Recognition. MLDM 2005. Lecture Notes in Computer Science(), vol 3587. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11510888_10

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  • DOI: https://doi.org/10.1007/11510888_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-26923-6

  • Online ISBN: 978-3-540-31891-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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