Sparse Proximal Support Vector Machine with a Specialized Interior-Point Method

Support vector machine(SVM)is a widely used method for classification.Proximal support vector machine(PSVM)is an extension of SVM and a promisingmethod to lead to a fast and simple algorithm for generating a classifier.Motivated by the fast computational efforts of PSVM and the properties of sparse solution yielded by l1-norm,in this paper,we first propose a PSVM with a cardinality constraint which is eventually relaxed byl1-norm and leads to a trade-offl1−l2 regularized sparse PSVM.Next we convert thisl1−l2 regularized sparse PSVM into an equivalent form of1 regularized least squares(LS)and solve it by a specialized interior-point method proposed by Kim et al.(J SelTop Signal Process 12:1932–4553,2007).Finally,l1−l2 regularized sparse PSVM is illustrated by means of a real-world dataset taken from the University of California,Irvine Machine Learning Repository(UCI Repository).Moreover,we compare the numerical results with the existing models such as generalized eigenvalue proximal SVM(GEPSVM),PSVM,and SVM-Light.The numerical results showthat thel1−l2 regularized sparsePSVMachieves not only better accuracy rate of classification than those of GEPSVM,PSVM,and SVM-Light,but also a sparser classifier compared with the1-PSVM.