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Support vector machines (SVMs) are learning algorithms derived from statistical learning theory, and originally designed to solve binary classification problems. How to effectively extend SVMs for multiclass classification problems is still an ongoing research issue. In this paper, a sphere-shaped SVM for multiclass problems is presented. Compared with the classical plane-shaped SVMs, the number of convex quadratic programming problems and the number of variables in each programming are smaller. Such SVM classifier is applied to the electroencephalogram (EEG) source localization problem, and the multiplicity of source models is determined according to the potentials recorded on the scalp. Experimental results indicate that the sphere-shaped SVM based classifier is an effective and promising approach for this task.