Multicategory SVMs by minimizing the distances among convex-hull prototypes

In this paper, we study a single objective extension of support vector machines for multicategory classification. Extending the dual formulation of binary SVMs, the algorithm looks for minimizing the sum of all the pairwise distances among a set of prototypes, each one constrained to one of the convex-hulls enclosing a class of examples. The final discriminant system is built looking for an appropriate reference point in the feature space. The obtained method preserves the form and complexity of the binary case, optimizing just one convex objective function with m variables and 2m+K constraints, where m is the number of examples and K the number of classes. Non-linear extension are straightforward using kernels while soft margin versions can be obtained by using reduced convex hulls. Experimental results in well-known UCI benchmarks are presented, comparing the accuracy and efficiency of the proposed approach with other state-of-the-art methods.