Computational Optimization and Applications

, Volume 12, Issue 1, pp 53–79

Multicategory Classification by Support Vector Machines

  • Erin J. Bredensteiner
  • Kristin P. Bennett

DOI: 10.1023/A:1008663629662

Cite this article as:
Bredensteiner, E.J. & Bennett, K.P. Computational Optimization and Applications (1999) 12: 53. doi:10.1023/A:1008663629662


We examine the problem of how to discriminate between objects of three or more classes. Specifically, we investigate how two-class discrimination methods can be extended to the multiclass case. We show how the linear programming (LP) approaches based on the work of Mangasarian and quadratic programming (QP) approaches based on Vapnik's Support Vector Machine (SVM) can be combined to yield two new approaches to the multiclass problem. In LP multiclass discrimination, a single linear program is used to construct a piecewise-linear classification function. In our proposed multiclass SVM method, a single quadratic program is used to construct a piecewise-nonlinear classification function. Each piece of this function can take the form of a polynomial, a radial basis function, or even a neural network. For the k > 2-class problems, the SVM method as originally proposed required the construction of a two-class SVM to separate each class from the remaining classes. Similarily, k two-class linear programs can be used for the multiclass problem. We performed an empirical study of the original LP method, the proposed k LP method, the proposed single QP method and the original k QP methods. We discuss the advantages and disadvantages of each approach.

support vector machines linear programming classification data mining machine learning. 

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • Erin J. Bredensteiner
    • 1
  • Kristin P. Bennett
    • 2
  1. 1.Department of MathematicsUniversity of EvansvilleEvansville
  2. 2.Department of Mathematical SciencesRensselaer Polytechnic InstituteTroy

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