Proving to the Coincidence of the Solutions of the Modified Problem with the Original Problem of Multi-class Support Vector Machine

Vojtech Franc and Vaclav Hlavac proposed a transformation from the multi-class support vector machine problem to the one-class support vector machine problem which is more convenient for optimization. Moreover, the proposed transformation can be performed by the properly defined kernel function only. The experiments conducted indicate that the proposed method is comparable with the one-against-all decomposition solved by the state-of-the-art sequential minimal optimizer algorithms. This paper proves strictly with theory that the solution of the one-class support vector machine problem coincides mostly with the solution of the multi-class support vector machine problem.