Adaptive ridge procedure for L0-penalized weighted support vector machine

Abstract

Although the L0-penalty is the most natural choice to identify the sparsity structure of the model, it has not been widely used due to the computational bottleneck. Recently, the adaptive ridge procedure is developed to efficiently approximate a Lq-penalized problem to an iterative L2-penalized one. In this article, we proposed to apply the adaptive ridge procedure to solve the L0-penalized weighted support vector machine (WSVM) to facilitate the corresponding optimization. Our numerical investigation shows the advantageous performance of the L0-penalized WSVM compared to the conventional WSVM with L2 penalty for both simulated and real data sets.