Active-Set Methods for Support Vector Machines

Abstract

This chapter describes an active-set algorithm for quadratic programming problems that arise from the computation of support vector machines (SVMs). Currently, most SVM optimizers implement working-set (decomposition)techniques because of their ability to handle large data sets. Although these show good results in general, active-set methods are a reasonable alternative - in particular if the data set is not too large, if the problem is ill-conditioned, or if high precision is needed. Algorithms are derived for classification and regression with both fixed and variable bias term. The material is completed by acceleration and approximation techniques as well as a comparison with other optimization methods in application examples.