Robust $L_{2,1}$ -Norm Distance Enhanced Multi-Weight Vector Projection Support Vector Machine

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.