A new iterative algorithm training SVM

Abstract

Based on the geometric interpretation of the support vector machine (SVM), a new feasible direction (NFD) algorithm is first proposed as a generalization of Franc and Hlaváĉ’s SK algorithm in this study. In the new algorithm, two vertices of the training sets are selected to update the current solution per iteration for the separable problem, while only one of them is used in the SK algorithm. Similar to the SK and Keerthi et al.’s nearest points algorithm (NPA), the proposed NFD can solve the inseparable problem with L 2 cost function. Furthermore, based on a geometric interpretation of ν-SVM and the definition of the reduced convex hull, the proposed algorithm extends to train the ν-SVM with commonly L 1 cost function for the inseparable problem. The convergence property of the algorithm is studied from the theoretical viewpoint. Computational experiments suggest that our algorithms are competitive with other SVM algorithms including SK, NPA, Tao et al.’s generalized SK and SMO. It was observed that the number of iterations and the training time are reduced in many cases.