Support vector machine classification with noisy data: a second order cone programming approach

In this paper, we investigate the stability of linear and quadratic programming support vector machines (SVMs) with bounded noise in the input data using a robust optimisation model. For a linear discriminant function, this model is expressed as a second order cone optimisation problem. Using the concept of the kernel function, we generalise for nonlinear discriminant functions. Intuitively, it looks quite clear that large margin classifiers are robust in terms of bounded input noise. However, there is no theoretical analysis investigating this behaviour. We show that the SVM solution is stable under bounded perturbations of the data both in the linear programming and quadratic programming. Computational results are also presented for toy and real-world data.