Multiobjective multiclass support vector machine based on the one-against-all method

Recently, some kinds of extensions of the binary support vector machine (SVM) to multiclass classification have been proposed. In this paper, we focus on the one-against-all and all-together methods, which finally construct the same kind of multiclass classifier. Since in the one-against-all method, binary SVMs are simply combined, the geometric margins of the multiclass classifier are not maximized. On the other hand, although the all-together method is aimed at maximizing the geometric margins for the generalization ability, it requires a large amount of computational resources because it is formulated as a large-scale optimization problem. In this paper, we propose a new model which constructs a multiclass classifier as a weighted combination of binary SVMs obtained by the one-against-all method and which maximizes the geometric margins. The proposed model can be expected to have the high generalization ability and reduce computational resources. Moreover, we show the advantage of the proposed model through numerical experiments.