It should be intuitively clear that when the underlying concept is defined by a polygonal space partitioning, it is preferable to use oblique decision trees for classification. For example, there exist many domains in which one or two oblique hyperplanes will be the best model to use for classification. The left side shows a simple 2-D domain in which two oblique hyperplanes define the classes. The right side shows an approximation of the sort that an axis-parallel decision tree would have to create to model this domain. The purpose of the current chapter is to review the strengths and weaknesses of some of the existing methods, to design a system that combines some of the strengths and overcomes the weaknesses, and to evaluate that system empirically and analytically.
Randomization helps significantly in learning many concepts.
Our algorithm is fully implemented as an oblique decision tree induction system and is available over the Internet. The ability to generate oblique trees often produces very small trees compared to axis-parallel methods. When the underlying problem requires an oblique split, oblique trees are also more accurate than axis-parallel trees. Section briefly reviews some existing techniques for oblique DT induction, outlines some limitations of each approach, and introduces the OC1 system. Section describes the OC1 system in detail.