Maximum margin classifiers with noisy data: a robust optimization approach

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