Robust L1-norm multi-weight vector projection support vector machine with efficient algorithm

The recently proposed multi-weight vector projection support vector machine (EMVSVM) is an excellent multi-projections classifier. However, the formulation of MVSVM is based on the L2-norm criterion, which makes it prone to be affected by outliers. To alleviate this issue, in this paper, we propose a robust L1-norm MVSVM method, termed as MVSVML1. Specifically, our MVSVML1 aims to seek a pair of multiple projections such that, for each class, it maximizes the ratio of the L1-norm between-class dispersion and the L1-norm within-class dispersion. To optimize such L1-norm ratio problem, a simple but efficient iterative algorithm is further presented. The convergence of the algorithm is also analyzed theoretically. Extensive experimental results on both synthetic and real-world datasets confirm the feasibility and effectiveness of the proposed MVSVML1.