Multicategory classification via discrete support vector machines

Discrete support vector machines (DSVM), originally proposed for binary classification problems, have been shown to outperform other competing approaches on well-known benchmark datasets. Here we address their extension to multicategory classification, by developing three different methods. Two of them are based respectively on one-against-all and round-robin classification schemes, in which a number of binary discrimination problems are solved by means of a variant of DSVM. The third method directly addresses the multicategory classification task, by building a decision tree in which an optimal split to separate classes is derived at each node by a new extended formulation of DSVM. Computational tests on publicly available datasets are then conducted to compare the three multicategory classifiers based on DSVM with other methods, indicating that the proposed techniques achieve significantly higher accuracies.