$\ell_{0}$-Norm Penalty Embedded Feature Selection in Universum Learning

Summary

This article introduces an $\ell_{0}$-norm penalty into the Universum support vector machine, so the classifier learns from an auxiliary unlabeled dataset within a lower-dimensional space made of the most relevant variables. The authors establish the existence of an optimal solution, derive necessary and sufficient optimality conditions using two types of stationary points, and develop an alternating direction method of multipliers algorithm whose convergence is shown under specific conditions. Numerical experiments across various datasets are reported as demonstrating the method's effectiveness.