Partitioning Nominal Attributes in Decision Trees

To find the optimal branching of a nominal attribute at a node in an L-ary decision tree, one is often forced to search over all possible L-ary partitions for the one that yields the minimum impurity measure. For binary trees (L = 2) when there are just two classes a short-cut search is possible that is linear in n, the number of distinct values of the attribute. For the general case in which the number of classes, k, may be greater than two, Burshtein et al. have shown that the optimal partition satisfies a condition that involves the existence of ( L 2 ) hyperplanes in the class probability space. We derive a property of the optimal partition for concave impurity measures (including in particular the Gini and entropy impurity measures) in terms of the existence of L vectors in the dual of the class probability space, which implies the earlier condition. Unfortunately, these insights still do not offer a practical search method when n and k are large, even for binary trees. We therefo...

• Type: Journal
• Year: 1999
• Where: DATAMINE
• Authors: Don Coppersmith, Se June Hong, Jonathan R. M. Hosking
• Keywords: Class Probability Space, DATAMINE 1999, Impurity Measures, Optimal Partition