The Support Vector Machine (SVM) has shown great performance in practice as a classification methodology. Oftentimes multicategory problems have been treated as a series of binary problems in the SVM paradigm. Even though the SVM implements the optimal classification rule asymptotically in the binary case, solutions to a series of binary problems may not be optimal for the original multicategory problem. We propose multicategory SVMs, which extend the binary SVM to the multicategory case, and encompass the binary SVM as a special case. The multicategory SVM implements the optimal classification rule as the sample size gets large, overcoming the suboptimality of the conventional one-versus-rest approach. The proposed method deals with the equal misclassification cost and the unequal cost case in unified way.
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