Abstract
The margin maximization principle implemented by binary Support Vector Machines (SVMs) has been shown to be equivalent to find the hyperplane equidistant to the closest points belonging to the convex hulls that enclose each class of examples. In this paper, we propose an extension of SVMs for multicategory classification which generalizes this geometric formulation. The obtained method preserves the form and complexity of the binary case, optimizing a single convex quadratic program where each new class introduces just one additional constraint. Reduced convex hulls and non-linear kernels, used in the binary case to deal with the non-linearly separable case, can be also implemented by our algorithm to obtain additional flexibility. Experimental results in well known datasets are presented, comparing our method with two widely used multicategory SVMs extensions.