Preprocessing Opportunities in Optimal Numerical Range Partitioning

We show that only the segment borders have to be taken into account as cut point candidates in searching for the optimal multisplit of a numerical value rangewith respect to convex attribute evaluation functions. Segment borders can be found efficiently in a linear-time preprocessing step. For strictly convex evaluation functions inspecting all segment borders is also necessary. With Training Set Error, which is not strictly convex, the data can be preprocessed into an even smaller number of cut point candidates, called alternations, when striving for optimal partition. Examining all alternations also seems necessary. We test empirically the reduction of the number of cut point candidates that can be obtained for Training Set Error on real-world data. The experiment shows that in some domains significant reduction in the number of cut point candidates can be obtained.