Selecting multiway splits in decision trees
Eibe Frank, Ian H. Witten · 1996
Abstract: Decision trees in which numeric attributes are split several ways are more comprehensible than the usual binary trees because attributes rarely appear more than once in any path from root to leaf. There are efficient algorithms for finding the optimal multiway split for a numeric attribute, given the number of intervals in which it is to be divided. The problem we tackle is how to choose this number in order to obtain small, accurate trees. We view each multiway decision as a model and a decision tree as a recursive structure of such models. Standard methods of choosing between competing models include resampling techniques (such as cross-validation, holdout, or bootstrap) for estimating the classification error; and minimum description length techniques. However, the recursive situation differs from the usual one, and may call for new model selection methods. This paper introduces a new criterion for model selection: a resampling estimate of the information gain. Empirical results are presented for building multiway decision trees using this new criterion, and compared with criteria adopted by previous authors. The new method generates multiway trees that are both smaller and more accurate than those produced previously, and their performance is comparable with standard binary decision trees.