Robust kernel-based multiclass support vector machines via second-order cone programming

摘要

Kernel methods are very important in pattern analysis due to their ability to capture nonlinear relationships in datasets. The best known kernel-based technique is Support Vector Machine (SVM), which can be used for several pattern recognition tasks, including multiclass classification. In this paper, we focus on maximum margin classifiers for nonlinear multiclass learning, based on second-order cone programming (SOCP), proposing three novel formulations that extend the most common strategies for this task: One-vs.-The-Rest, One-vs.-One, and All-Together optimization. The proposed SOCP formulations achieved superior performance compared to their traditional SVM counterparts on benchmark datasets, demonstrating the virtues of robust optimization.