Multicategory Classification by Support Vector Machines

Authors:
Erin J. Bredensteiner;Kristin P. Bennett
Affiliations:
Department of Mathematics, University of Evansville, Evansville, IN 47722. eb6@evansville.edu;Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180. bennek@rpi.edu
Venue:
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part I
Year:
1999

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Abstract

We examine the problem of how to discriminate between objectsof three or more classes. Specifically, we investigate how two-classdiscrimination methods can be extended to the multiclass case. Weshow how the linear programming (LP) approaches based on the work ofMangasarian and quadratic programming (QP) approaches based onVapnik‘s Support Vector Machine (SVM) can be combined to yield twonew approaches to the multiclass problem. In LP multiclassdiscrimination, a single linear program is used to construct apiecewise-linear classification function. In our proposed multiclassSVM method, a single quadratic program is used to construct apiecewise-nonlinear classification function. Each piece of thisfunction can take the form of a polynomial, a radial basis function,or even a neural network. For the k 2-class problems, the SVMmethod as originally proposed required the construction of atwo-class SVM to separate each class from the remaining classes.Similarily, k two-class linear programs can be used for themulticlass problem. We performed an empirical study of the originalLP method, the proposed k LP method, the proposed single QP methodand the original k QP methods. We discuss the advantages anddisadvantages of each approach.