Robust Support Vector Machine

In real world applications, the training data are not usually assumed to be known exactly due to measurement and statistical errors. Since the solutions to optimization problems are typically sensitive to training data perturbations, errors in the input data tend to get amplified in the decision function, often resulting in far from optimal solutions. So it will be useful to explore formulations that can yield robust discriminants to such estimation errors. In this chapter, we first established robust versions of SVORM, which are represented as a second order cone programming (SOCP). And as the theoretical foundation, we study the relationship between the solutions of the SOCP and its dual problem. Here the second order cone in Hilbert space is involved. Then, we also establish a multi-class algorithm based on the above robust SVORM for general multi-class classification problem with perturbations. Furthermore, we construct a robust unsupervised and semi-supervised SVC for the problems with uncertainty information.