Affiliations: [a] Federico Santa María University, CP 110-V Valparaíso, Chile | [b] European Centre for Soft Computing 33600 Mieres, Asturias, Spain | [c] Technical University of Dortmund, 44221 Dortmund, Germany
Note: [1] This work was supported by the Research Grant Fondecyt 1070220, Chile. The work of C. Moraga was partially supported by the Foundation for the Advancement of Soft Computing, Mieres Spain.
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.
