Multi-Objective Programming in SVMs

We propose a general framework for support vector machines (SVM) based on the principle of multi-objective optimization. The learning of SVMs is formulated as a multiobjective program by setting two competing goals to minimize the empirical risk and minimize the model capacity. Distinct approaches to solving the MOP introduce various SVM formulations. The proposed framework enables a more effective minimization of the VC bound on the generalization risk. We develop a feature selection approach based on the MOP framework and demonstrate its effectiveness on hand-written digit data.