The robust support vector machines (RoSVM) for ellipsoidal data is difficult to solve. To overcome this difficulty, its primal form has been approximated with a second-order cone programming (SOCP) called approximate primal RoSVM. In this article, we show that the primal RoSVM is equivalent to an SOCP and name it accurate primal RoSVM. The optimal weight vector of this model is not sparse necessarily. The sparser the weight vector, the less time the test phase takes. Hence, to reduce the test time, first, we obtain its dual form and then prove the sparsity of its optimal solution. Second, we show that some parts of the optimal decision function can be computed in the training phase instead of the test phase. This can decrease the test time further. However, training time of the dual model is more than that of the primal model, but the test time is often more critical than the training time because the training is often an off-line procedure while the test procedure is performed online. Experimental results on benchmark data sets show the superiority of the proposed models.

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