Active-Set Methods for Support Vector Machines

This chapter describes an active-set algorithm for the solution of quadratic programming problems in the context of Support Vector Machines (SVMs). Most of the common SVM optimizers implement working-set algorithms like the SMO method because of their ability to handle large data sets. Although they show generally good results, they may perform weakly in some situations, e.g., if the problem is ill-posed or if high precision is needed. In these cases, active-set techniques (which are robust general-purpose QP solvers) are a reasonable alternative. Algorithms are derived for classification and regression problems for both fixed and variable bias term. The approximation of the solution is considered as well as the comparison with other optimization methods.