A cutting plane algorithm for multiclass kernel discriminations

The problem of multiclass discrimination consists in classifying patterns into a set of finite classes. Usually, a multiclass problem is decomposed into multiple binary ones and the results of the binary problems are integrated for multiclass discrimination. These discriminators, however, could result in multi-classified and/or unclassified points. Therefore, we need some tie breaking mechanisms to handle the conflict. There exist several approaches which generate all discrimi- nators in one optimization problem. In this paper, we consider the formulation introduced by Crammer and Singer (3). They introduce a quadratic programming problem with a very large number of variables which is hard to optimize. Using a cutting plane procedure, we propose a new algorithm which solves the problem in a finite number of iterations. The results of experiments on five datasets show that the proposed method achieves higher classification performance than the traditional methods by using binary algorithms.