Multivariate classification trees based on minimum features discrete support vector machines

A variant of support vector machines is proposed in which the empirical error is expressed as a discrete measure, by counting the number of misclassified instances, and an additional term is considered in order to reduce the complexity of the rule generated. This leads to the formulation of a mixed integer programming problem, solved via a sequential LP-based heuristic. We then devise a procedure for generating decision trees in which a multivariate splitting rule is derived at each node from the approximate solution of the proposed discrete SVM. Computational tests are performed on several benchmark datasets and three large real-world marketing datasets. They indicate that our classifier is more accurate than other well-known methods. It is also empirically shown that discrete SVMs dominate their continuous counterpart when framed within the decision tree algorithm.