Second Order Cone Programming Formulations for Handling Data with Perturbation

Ordinal regression problem and general multi-class classification problem are important and on-going research subject in machine learning. Support vector ordinal regression machine (SVORM) is an effective method for ordinal regression problem and has been used to deal with general multi-class classification problem. Up to now it is always assumed implicitly that the training data are known exactly . However, in practice, the training data subject to measurement noise. In this paper, we propose the robust versions of SVORM. Furthermore, we also propose a robust multi-class algorithm based on 3-class robust SVORM with Gaussian kernel for general multi-class classification problem with perturbation. The robustness of the proposed methods is validated by our preliminary numerical experiments.