A New Smooth Support Vector Machine with 1-Norm Penalty Term

Abstract

Recently, soft margin smooth support vector machine with 1-norm penalty term (SSVM1) is discovered to possess better outlier resistance than soft margin smooth support vector machine with 2-norm penalty term (SSVM2). One of the most important steps in the framework of SSVMs is to replace the x+ by a differential function in the primal model, and get an approximate solution. This study proposes one function constructed by Padé approximant via the formal orthogonal polynomials as the smoothing technique, and a new 1-norm SSVM, Padé SSVM1, is represented. A method for outlier filtering is proposed to improve the ability of outlier resistance. The experimental results show that Padé SSVM1, even without outlier filtering, performs better than the previous SSVM2 and SSVM1 on the polluted synthetic datasets.