Fast Algorithms for Linear and Kernel SVM+

Abstract

The SVM+ approach has shown excellent performance in visual recognition tasks for exploiting privileged information in the training data. In this paper, we propose two efficient algorithms for solving the linear and kernel SVM+, respectively. For linear SVM+, we absorb the bias term into the weight vector, and formulate a new optimization problem with simpler constraints in the dual form. Then, we develop an efficient dual coordinate descent algorithm to solve the new optimization problem. For kernel SVM+, we further apply the l2-loss, which leads to a simpler optimization problem in the dual form with only half of dual variables when compared with the dual form of the original SVM+ method. More interestingly, we show that our new dual problem can be efficiently solved by using the SMO algorithm of the one-class SVM problem. Comprehensive experiments on three datasets clearly demonstrate that our proposed algorithms achieve significant speed-up than the state-of-the-art solvers for linear and kernel SVM+.