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 L2,1-norm distance (L2,1-EMVSVM). The distances in the objective of our algorithm are measured by the L2,1-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 L2,1-EMVSVM are verified through extensive experiments.

Keywords

• L₂,₁-norm
• L₂-norm
• EMVSVM
• robustness