Algorithms for finding attribute value group for binary segmentation of categorical databases

We consider the problem of finding a set of attribute values that give a high quality binary segmentation of a database. The quality of a segmentation is defined by an objective function suitable for the user\´s objective, such as "mean squared error," "mutual information," or "χ²" each of which is defined in terms of the distribution of a given target attribute. Our goal is to find value groups on a given conditional domain that split databases into two segments, optimizing the value of an objective function. Though the problem is intractable for general objective functions, there are feasible algorithms for finding high quality binary segmentations when the objective function is convex, and we prove that the typical criteria mentioned above are all convex. We propose two practical algorithms, based on computational geometry techniques, which find a much better value group than conventional heuristics.