Elastic net twin support vector machine and its safe screening rules

Abstract

In this paper, we present a new classifier called elastic net twin support vector machine (ETSVM). It resolves two smaller-sized quadratic programming problems (QPPs) similarly to the twin support vector machine (TSVM). The key difference between them is that ETSVM uses elastic net penalty for slack variables, which enhances classification performance. The dual QPPs of the ETSVM do not involve matrix inversion, in contrast to conventional TSVM. As a result, ETSVM can avoid the ill-conditioning case. We theoretically discuss its properties, including exploring the violation tolerance upper bound for the two QPPs of ETSVM. In order to increase computing efficiency, we derive a sequence of safe screening rules using variational inequalities to quicken the ETSVM parameter tuning process (SSR-ETSVM). We compare the proposed algorithm with SVM, nonparallel hyperplane SVM, elastic net SVM, and elastic net nonparallel hyperplane SVM. Numerical experiments confirm the rationality and effectiveness of the proposed methods.