Quasi-monotone decision trees for ordinal classification

In many classification problems the domains of the attributes and the classes are linearly ordered. Since the known decision tree methods generate non-monotone trees, these methods are not suitable for monotone classification problems. We already provided order-preserving tree-generation algorithms for multi-attribute classification problems with k linearly ordered classes in a previous paper. For real-world datasets it is important to consider approximate solutions to handle problems like speed, tree-size and noise. In this report we develop a new decision tree algorithm that generates quasi-monotone decision trees. This algorithm outperforms classical algorithms such as those of Quinlan with respect to prediction, and beats algorithms that generate strictly monotone decision trees with respect to speed. This report contains proofs of all presented results.