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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{2}$ </tex-math></inline-formula> -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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2,1</sub> -norm distance (L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2,1</sub> -EMVSVM). The distances in the objective of our algorithm are measured by the L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2,1</sub> -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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2,1</sub> -EMVSVM are verified through extensive experiments.