Proximal Support Vector Machine with Mixed Norm

Proximal Support Vector Machine with Mixed Norm

This paper proposes a new version of support vector machine (SVM) for binary classification named mixed norm proximal support vector machine, MPSVM for short. By introducing the p-norm of the normal vector of the classification hyper-plane into the objective function of proximal SVM, we get the objective function of MPSVM. MPSVM is an adaptive learning procedure with p-norm (0 < p < 1), where p can be automatically chosen by data. By adjusting the parameter p, MPSVM can realize feature selection and classification simultaneously. Since the optimization problem of MBPSVM is neither convex nor differentiable, an iterative algorithm is used to solve it. Experiments carried out on several standard UCI datasets show a clear improvement over some popular methods.