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We study a multiclass extension of support vector machine (SVM) based on geometric margin maximization. Since there are different margins for different class-pairs, the maximum-margin SVM can be formulated as a multiobjective optimization problem. This multiobjective multiclass SVM (MMSVM) is difficult to be solved because not only it is multiobjective but also it is nonconvex. In order to solve the MMSVM, we approximate it by a convex multiobjective problem, and furthermore scalarize its objective functions. In this paper, we propose a new scalarization for MMSVM using the large-k norm, which provides a spectrum between the `∞ and `1 norms.

Scalarization for Approximate Multiobjective Multiclass Support Vector Machine Using the Large-k Norm