A multiclass decision rule minimizing a loss function based on one class SVM

A multiclass algorithm based on nu-1-SVM which minimizes a loss function is introduced. The loss function allows to use decision costs which depend on the classes, and to consider partial and total rejection. The algorithm is based on deriving the nu-1 SVM regularization path for each class. The decision rule is determined by tuning all the nu-1-SVM parameters and all the other decision parameters together in order to minimize the loss function. Experimental results on artificial data sets and some benchmark data sets are provided to assess the effectiveness of this approach.