Sparse L0-norm least squares support vector machine with feature selection

Abstract

Least squares support vector machine (LSSVM) is a powerful classification tool based on hyperplanes. But the classical LSSVM does not perform well on small sample size data sets (SSS) because it lacks feature selection capability. To address this issue, we introduce an L0-norm regularization term into the objective function of LSSVM, and propose a new sparse LSSVM model called L0-LSSVM. However, the introduction of the L0-norm makes the resulting optimization problem nonconvex and nonsmooth. To overcome these challenges, instead of using the traditional convex or non-convex approximation of the L0-norm, we design an efficient algorithm for L0-LSSVM based on alternating direction method of multipliers (ADMM) where the L0-norm is handled by employing the proximity operator. Numerical results demonstrate that L0-LSSVM not only exhibits excellent generalization performance and feature selection capability but also offers a substantial improvement in computational speed.