An Efficient Implementation of an Active Set Method for SVMs

We propose an active set algorithm to solve the convex quadratic programming (QP) problem which is the core of the support vector machine (SVM) training. The underlying method is not new and is based on the extensive practice of the Simplex method and its variants for convex quadratic problems. However, its application to large-scale SVM problems is new. Until recently the traditional active set methods were considered impractical for large SVM problems. By adapting the methods to the special structure of SVM problems we were able to produce an efficient implementation. We conduct an extensive study of the behavior of our method and its variations on SVM problems. We present computational results comparing our method with Joachims’ SVMlight (see Joachims, 1999). The results show that our method has overall better performance on many SVM problems. It seems to have a particularly strong advantage on more difficult problems. In addition this algorithm has better theoretical properties and it naturally extends to the incremental mode. Since the proposed method solves the standard SVM formulation, as does SVMlight , the generalization properties of these two approaches are identical and we do not discuss them in the paper.