Multi-objective Multiclass Support Vector Machine for Pattern Recognition

Support vector machines were originally proposed for the binary classification. For multiclass classification, some kinds of extensions of SVMs have been proposed. In this paper, we focus on "all together" method, where an extended SVM is constructed by using a piece-wise linear function. This model is formulated as an optimization problem which maximizes margins between each pair of classes for the generalization ability. However, as we point out in this paper, the model does not correctly represent the margins. Therefore, we propose a multi-objective model which exactly maximizes all margins. In addition, we derive a new SVM as a single-objective quadratic programming problem and apply the proposed SVM to some problems and verify its efficiency.