Pruning for Monotone Classification Trees

For classification problems with ordinal attributes very often the class attribute should increase with each or some of the explanatory attributes. These are called classification problems with monotonicity constraints. Standard classification tree algorithms such as CART or C4.5 are not guaranteed to produce monotone trees, even if the data set is completely monotone. We look at pruning based methods to build monotone classification trees from monotone as well as nonmonotone data sets. We develop a number of fixing methods, that make a non-monotone tree monotone by additional pruning steps. These fixing methods can be combined with existing pruning techniques to obtain a sequence of monotone trees. The performance of the new algorithms is evaluated through experimental studies on artificial as well as real life data sets. We conclude that the monotone trees have a slightly better predictive performance and are considerably smaller than trees constructed by the standard algorithm.