Data abstractions for numerical attributes in data mining

Abstract

In this paper, we investigate data abstractions for mining association rules with numerical conditions and boolean consequents as a target class. The act of our abstraction corresponds to joining some consecutive primitive intervals of a numerical attribute. If the interclass variance for two adjacent intervals is less than a given admissible upper-bound ∈, then they are combined together into an extended interval. Intuitively speaking, a low value of the variance means that the two intervals can provide almost the same posterior class distributions. This implies few properties or characteristics about the class would be lost by combining such intervals together. We discuss a bottom-up-method for finding maximally extended intervals, called maximal appropriate abstraction. Based on such an abstraction, we can reduce the number of extracted rules, still preserving almost the same quality of the rules extracted without abstractions. The usefulness of our abstraction method is shown by preliminary experimental results.