Well-Behaved Evaluation Functions for Numerical Attributes
The class of well-behaved evaluation functions simplifies and makes efficient the handling of numerical attributes; for them it suffices to concentrate on the boundary points in searching for the optimal partition. This holds always for binary partitions and also for multisplits if only the function is cumulative in addition to being well-behaved. A large portion of the most important attribute evaluation functions are well-behaved. This paper surveys the class of well-behaved functions. As a case study, we examine the properties of C4.5's attribute evaluation functions. Our empirical experiments show that a very simple cumulative rectification to the poor bias of information gain significantly outperforms gain ratio.