System Evaluation of Construction Methods for Multi-class Problems Using Binary Classifiers

  • Shigeichi Hirasawa
  • Gendo Kumoi
  • Manabu Kobayashi
  • Masayuki Goto
  • Hiroshige Inazumi
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 746)


Construction methods for multi-valued classification (multi-class) systems using binary classifiers are discussed and evaluated by a trade-off model for system evaluation based on rate-distortion theory. Suppose the multi-class systems consisted of \(M (\ge 3)\) categories and \(N (\ge M-1)\) binary classifiers, then they can be represented by a matrix W, where the matrix W is given by a table of M code words with length N, called a code word table. For a document classification task, the relationship between the probability of classification error \(P_e\) and the number of binary classifiers N for given M is investigated, and we show that our constructed systems satisfy desirable properties such as “Flexible”, and “Elastic”. In particular, modified Reed Muller codes perform well: they are shown to be “Effective elastic”. As a second application we consider a hand-written character recognition task, and we show that the desirable properties are also satisfied.


Multi-valued classification Binary classifier Trade-off model ECOC Exhaustive code Error correcting codes 



One of the authors S. H. would like to thank Professor Shin’ ichi Oishi of Waseda University for giving a chance to study this work. The research leading to this paper was partially supported by MEXT Kakenhi under Grant-in Aids for Scientific Research (B) No. 26282090 and (C) No. 16K00491.


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Shigeichi Hirasawa
    • 1
  • Gendo Kumoi
    • 2
  • Manabu Kobayashi
    • 3
  • Masayuki Goto
    • 4
  • Hiroshige Inazumi
    • 5
  1. 1.Research Institute for Science and EngineeringWaseda UniversityTokyoJapan
  2. 2.Graduate School of Creative Science and EngineeringWaseda UniversityTokyoJapan
  3. 3.Faculty of EngineeringShonan Institute of TechnologyFujisawaJapan
  4. 4.School of Creative Science and EngineeringWaseda UniversityTokyoJapan
  5. 5.Faculty of InformaticsAoyama Gakuin UniversityTokyoJapan

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