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.