Relationships among various parameters for decision tree optimization

In this chapter, we study, in detail, the relationships between various pairs of cost functions and between uncertainty measure and cost functions, for decision tree optimization. We provide new tools (algorithms) to compute relationship functions, as well as provide experimental results on decision tables acquired from UCI ML Repository. The algorithms presented in this paper have already been implemented and are now a part of Dagger, which is a software system for construction/optimization of decision trees and decision rules. The main results presented in this chapter deal with two types of algorithms for computing relationships; first, we discuss the case where we construct approximate decision trees and are interested in relationships between certain cost function, such as depth or number of nodes of a decision trees, and an uncertainty measure, such as misclassification error (accuracy) of decision tree. Secondly, relationships between two different cost functions are discussed, for example, the number of misclassification of a decision tree versus number of nodes in a decision trees. The results of experiments, presented in the chapter, provide further insight. © 2014 Springer International Publishing Switzerland.