Lp-norm proximal support vector machine and its applications

Abstract

In this paper, we propose an efficient l p -norm ( 0 < p < 1 ) Proximal Support Vector Machine by combining proximal support vector machine (PSVM) and feature selection strategy together. Following two lower bounds for the absolute value of nonzero entries in every local optimal solution of the model, we investigate the relationship between sparsity of the solution and the choice of the regularization parameter and p -norm. After smoothing the problem in l p -norm PSVM, we solved it by smoothing conjugate gradient method (SCG) method, and preliminary numerical experiments show the effectiveness of our model for identifying nonzero entries in numerical solutions and feature selection, and we also apply it to a real-life credit dataset to prove its efficiency.