Kernel Projection Algorithm for Large-Scale SVM Problems

Support Vector Machine (SVM) has become a very effective method instatistical machine learning and it has proved that training SVM is tosolve Nearest Point pair Problem (NPP) between two disjoint closedconvex sets. Later Keerthi pointed out that it is difficult to applyclassical excellent geometric algorithms directly to SVM and sodesigned a new geometric algorithm for SVM. In this article, a newalgorithm for geometrically solving SVM, Kernel Projection Algorithm, ispresented based on the theorem on fixed-points of projection mapping.This new algorithm makes it easy to apply classical geometric algorithmsto solving SVM and is more understandable than Keerthi's. Experimentsshow that the new algorithm can also handle large-scale SVMproblems. Geometric algorithms for SVM, such as Keerthi's algorithm,require that two closed convex sets be disjoint and otherwise thealgorithms are meaningless. In this article, this requirementwill be guaranteed in theory by using the theoretic result on universalkernel functions.