Robust Nonparallel Proximal Support Vector Machine With Lp-Norm Regularization

As a useful classification method, generalized eigenvalue proximal support vector machine (GEPSVM) is recently studied extensively. However, it may suffer from the sensitivity to outliers, since the L2-norm is used as a measure distance. In this paper, based on the robustness of the L1-norm, we propose an improved robust L1-norm nonparallel proximal SVM with an arbitrary Lp-norm regularization (LpNPSVM), where p > 0. Compared with GEPSVM, the LpNPSVM is more robust to outliers and noise. A simple but effective iterative technique is introduced to solve the LpNPSVM, and its convergence guarantee is also given when 0 < p <= 2. Experimental results on different types of contaminated data sets show the effectiveness of LpNPSVM. At last, we investigate our LpNPSVM on a real spare parts inspection problem. Computational results demonstrate the effectiveness of the proposed method over the GEPSVM on all the noise data.