A Metric Approach to Building Decision Trees Based on Goodman-Kruskal Association Index

We introduce a numerical measure on sets of partitions of finite sets that is linked to the Goodman-Kruskal association index commonly used in statistics. This measure allows us to define a metric on such partions used for constructing decision trees. Experimental results suggest that by replacing the usual splitting criterion used in C4.5 by a metric criterion based on the Goodman-Kruskal coefficient it is possible, in most cases, to obtain smaller decision trees without sacrificing accuracy.