A Multiclass Robust Twin Parametric Margin Support Vector Machine with an Application to Vehicles Emissions

This paper considers the problem of predicting vehicles smog rating by applying a novel Support Vector Machine (SVM) technique. Classical SVM-type models perform a binary classification of the training observations. However, in many real-world applications only two classifying categories may not be enough. For this reason, a new multiclass Twin Parametric Margin Support Vector Machine (TPMSVM) is designed. On the basis of different characteristics, such as engine size and fuel consumption, the model aims to assign each vehicle to a specific smog rating class. To protect the model against uncertainty arising in the measurement procedure, a robust optimization extension of the multiclass TPMSVM model is formulated. Spherical uncertainty sets are considered and a tractable robust counterpart of the model is derived. Experimental results on a real-world dataset show the good performance of the robust formulation.