A Sequential Minimal Optimization Algorithm for the All-Distances Support Vector Machine ⋆ Diego Candel 1 , Ricardo ˜ Nanculef 1 , Carlos Concha 1 , and H´ ector Allende 1,2 1 Universidad T´ ecnica Federico Santa Mar´ ıa, Departamento de Inform´ atica, CP 110-V Valpara´ ıso, Chile {dcontard,jnancu,cconcha,hallende}@inf.utfsm.cl 2 Universidad Adolfo Ib´a˜ nez, Facultad de Ingenier´ ıa y Ciencia, Santiago, Chile hallende@uai.cl Abstract. The All-Distances SVM is a single-objective light extension of the binary μ-SVM for multi-category classification that is competitive against multi-objective SVMs, such as One-against-the-Rest SVMs and One-against-One SVMs. Although the model takes into account consid- erably less constraints than previous formulations, it lacks of an efficient training algorithm, making its use with medium and large problems im- practicable. In this paper, a Sequential Minimal Optimization -like algo- rithm is proposed to train the All-Distances SVM, making large prob- lems abordable. Experimental results with public benchmark data are presented to show the performance of the AD-SVM trained with this algorithm against other single-objective multi-category SVMs. Keywords: Kernel Machines, Multi-category Classification, Support Vector Machines, Sequential Minimal Optimization. 1 Introduction Support Vector Machines [20] (SVMs) are currently well known methods for pattern recognition and other data analysis, with strong theoretical properties and practical results when applied to real-world problems. Originally formulated to deal with linearly separable binary classification problems, they can also deal with noisy data and non-linearly separable cases using a regularization and a kernel method extension respectively. Although the training of these machines can be assumed as finding the so- lution to a quadratic optimization problem with linear restrictions, traditional approaches are impractical due to the dense nature of the Hessian Matrix in- volved in the problem definition. To deal with this, chunking and decomposition algorithms have been proposed through time, being the Sequential Minimal Op- timization (SMO) [18,14,10] one of the most popular methods employed for this purpose. ⋆ This work was supported in part by Research Grant FB0821 “Centro Cient´ ıfico Tecnol´ogicodeValpara´ ıso” UTFSM and by DGIP-UTFSM Grant. I. Bloch and R.M. Cesar, Jr. (Eds.): CIARP 2010, LNCS 6419, pp. 484–491, 2010. c  Springer-Verlag Berlin Heidelberg 2010