Approximate Multiobjective Multiclass SVM by Using the Reference Point Method
Yasuhiro Matsugi, Takafumi Sugimoto, Yuxiao Qi, Yoshifumi Kusunoki, Keiji Tatsumi · 2018
The support vector machine (SVM) for multiclass classification problem has attracted attention in recent years. We focus on the multiobjective multiclass SVM (MMSVM), which maximizes accurately the geometric margins of pairwise classes. The MMSVM was reported to obtain a classifier with a high generalization ability, while it requires a lot of computational resources because its training requires solving a nonconvex multiobjective optimization problem (MO). In this paper, we propose the approximate MMSVM, in which the nonconvex MO is approximated by a convex one, and the convex problem is solved by the reference point method while considering the balance between the geometric margins. The reference point method uses the reference point and weights which are selected on the basis of the distances between centroids or the one-against-one margins. Through numerical experiments, we show that the proposed method can reduce required computational resources, and can achieve a high generalization ability.