A Supervised Decision Rule for Multiclass Problems Minimizing a Loss Function

A multiclass learning method which minimizes a loss function is proposed. The loss function is defined by costs associated to the decision options which may include classes, subsets of classes if partial rejection is considered and all classes if total rejection is introduced. A formulation of the general problem is given, a decision rule which is based on the v-1-SVMs trained on each class is defined and a learning method is proposed. This latter optimizes all the v-1-SVM parameters and all the decision rule parameters jointly in order to minimize the loss function. To extend the search space of the v-1-SVM parameters and keep the processing time under control, the v-1-SVM regularization path is derived for each class and used during the learning process. Experimental results on artificial data sets and some benchmark data sets are provided to assess the effectiveness of the approach.