A novel multi-class SVM model using second-order cone constraints

In this work we present a novel maximum-margin approach for multi-class Support Vector Machines based on second-order cone programming. The proposed method consists of a single optimization model to construct all classification functions, in which the number of second-order cone constraints corresponds to the number of classes. This is a key difference from traditional SVM, where the number of constraints is usually related to the number of training instances. This formulation is extended further to kernel-based classification, while the duality theory provides an interesting geometric interpretation: the method finds an equidistant point between a set of ellipsoids. Experiments on benchmark datasets demonstrate the virtues of our method in terms of predictive performance compared with various other multicategory SVM approaches.