Robust <inline-formula> <tex-math notation="LaTeX">$L_{2,1}$ </tex-math> </inline-formula>-Norm Distance Enhanced Multi-Weight Vector Projection Support Vector Machine

Abstract

The enhanced multi-weight vector projection support vector machine (EMVSVM) is an outstanding algorithm for binary classification, which is proposed recently. However, it measures the distances in an objective function by the squared L 2-norm, which exaggerates the effects of outliers or noisy data. In order to alleviate this problem, we propose an effective novel EMVSVM, termed robust EMVSVM based on the L 2,1-norm distance (L 2,1-EMVSVM). The distances in the objective of our algorithm are measured by the L 2,1-norm. Besides, a new powerful iterative algorithm is designed to solve the formulated objective, whose convergence is ensured by theoretical proofs. Finally, the effectiveness and robustness of L 2,1-EMVSVM are verified through extensive experiments.