An Application of Approximated Entropy Measures in Decision Tree Induction

The main task in decision tree construction algorithms is to find the ”best partition” of set of objects. We consider the problem of searching for optimal binary partition of continuous attribute domain for large data sets stored in relational data bases (RDB). The straightforward approach to optimal partition selection with respect to entropy measure (which evaluates the quality of a partition) needs O(N) simple queries, where N is the number of pre-assumed partitions. We present new approximated entropy measures that allow to construct the partition very close to optimal, using only O(logN) simple queries.