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Support Vector Machine for Multiclass Classification

Support vector machines (SVMs) are primarily designed for 2-class classification problems. Although in several papers it is mentioned that the combination of $K$ SVMs can be used to solve a $K$-class classification problem, such a procedure requires some care. In this paper, the scaling problem of different SVMs is highlighted. Various normalization methods are proposed to cope with this problem and their efficiencies are measured empirically. This simple way of using SVMs to learn a $K$-class classification problem consists in choosing the maximum applied to the outputs of $K$ SVMs solving a \textit{one-per-class} decomposition of the general problem. In the second part of this paper, more sophisticated techniques are suggested. On the one hand, a stacking of the $K$ SVMs with other classification techniques is proposed. On the other end, the \textit{one-per-class} decomposition scheme is replaced by more elaborated schemes based on error-correcting codes. An incremental algorithm for the elaboration of pertinent decomposition schemes is mentioned, which exploits the properties of SVMs for an efficient computation.

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