Robust classification and regression using support vector machines

In this paper, we investigate the theoretical aspects of robust classification and robust regression using support vector machines. Given training data (x1, y1), … , (xl, yl), where l represents the number of samples, xi ∈ ℝⁿ and yi ∈ {−1, 1} (for classification) or yi ∈ ℝ (for regression), we investigate the training of a support vector machine in the case where bounded perturbation is added to the value of the input xi ∈ ℝⁿ. We consider both cases where our training data are either linearly separable and nonlinearly separable respectively. We show that we can perform robust classification or regression by using linear or second order cone programming.