Safe sample screening rules for multicategory angle-based support vector machines

Support vector machines are popular techniques for classification problems, where the optimal separating hyperplane only depends on a subset of training data. To reduce computational costs, safe sample screening rules are proposed in the literature, which enable us to remove redundant samples prior to the training phase. However, existing works on safe sample screening rules mainly focus on binary classification. The multicategory angle-based support vector machine (MASVM) is a computationally efficient method for multicategory classification problems, which constructs a decision function without the sum-to-zero constraint. To further reduce computational costs in linear MASVM, two safe sample screening methods are proposed: the gap safe rule (MAGSR) and the dual screening with variational inequalities (MADVI). A two-stage screening framework combining MAGSR and MADVI together is then developed. Extensive simulations and real applications show the great advantage of the proposed methods in computation, compared with existing approaches.