Robust Nonparallel Proximal Support Vector Machine With Lp-Norm Regularization

• Published in: IEEE access Vol. 6; pp. 20334 - 20347
• Main Authors: Sun, Xiao-Quan, Chen, Yi-Jian, Shao, Yuan-Hai, Li, Chun-Na, Wang, Chang-Hui
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 2018; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Classification algorithms; Convergence; Eigenvalues; Eigenvalues and eigenfunctions; Inspection; Iterative methods; Lp-norm; Optimization; Outliers (statistics); Regularization; Robustness; Sensitivity; Spare parts; Support vector machines; Training
• ISSN: 2169-3536; 2169-3536
• DOI: 10.1109/ACCESS.2018.2822546

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 <inline-formula> <tex-math notation="LaTeX">p>0 </tex-math></inline-formula>. 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 <inline-formula> <tex-math notation="LaTeX">0<p\leq 2 </tex-math></inline-formula>. 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.