Classifier Selection in a Family of Polyhedron Classifiers

  • Tetsuji Takahashi
  • Mineichi Kudo
  • Atsuyoshi Nakamura
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5856)


We consider an algorithm to approximate each class region by a small number of convex hulls and to apply them to classification. The convex hull of a finite set of points is computationally hard to be constructed in high dimensionality. Therefore, instead of the exact convex hull, we find an approximate convex hull (a polyhedron) in a time complexity that is linear in dimension. On the other hand, the set of such convex hulls is often too much complicated for classification. Thus we control the complexity by adjusting the number of faces of convex hulls. For reducing the computational time, we use an upper bound of the leave-one-out estimated error to evaluate the classifiers.


Support Vector Machine Convex Hull Testing Error Support Plane Class Region 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Kudo, M., Shimbo, M.: Appriximation of class region by convex hulls. Technical report of IEICE. PRMU 100, 1–6 (2000) (in Japanese)Google Scholar
  2. 2.
    Collobert, R., Bengio, S.: SVMTorch: support vector machines for large-scale regression problems. Journal of Machine Learning Research 1, 143–160 (2001)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Kudo, M., Takigawa, I., Nakamura, A.: Classification by reflective convex hulls. In: Proceedings of 19th International Conference on Pattern Recognision (ICPR 2008), Tampa, Florida, USA (2008)Google Scholar
  4. 4.
    Ghosh, P., Kumar, K.: Support function representation of convex bodies, its application in geometric computing, and some related representations. Computer Vision and Image Understanding 72, 379–403 (1998)CrossRefGoogle Scholar
  5. 5.
    Asuncion, A., Newman, D.: UCI machine learning repository (2007)Google Scholar
  6. 6.
    Zhou, D., Xiao, B., Zhou, H.: Global geometry of svm classifiers. Technical report, AI Lab, Institute of Automation, Chinese Academy of Sciences (2002)Google Scholar
  7. 7.
    Theodoridis, S., Mavroforakis, M.: Reduced convex hulls: A geometric approach to support vector machines. IEEE Signal Processing Magazine 1 (2007)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Tetsuji Takahashi
    • 1
  • Mineichi Kudo
    • 1
  • Atsuyoshi Nakamura
    • 1
  1. 1.Division of Computer Science Information Science and TechnologyHokkaido UniversitySapporoJapan

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