Speeding Up the Search for Optimal Partitions

Numerical value range partitioning is an inherent part of inductive learning. In classification problems, a common partition ranking method is to use an attribute evaluation function to assign a goodness score to each candidate. Optimal cut point selection constitutes a potential efficiency bottleneck, which is often circumvented by using heuristic methods.

This paper aims at improving the efficiency of optimal multisplitting. We analyze convex and cumulative evaluation functions, which account for the majority of commonly used goodness criteria. We derive an analytical bound, which lets us filter out—when searching for the optimal multisplit—all partitions containing a specific subpartition as their prefix. Thus, the search space of the algorithm can be restricted without losing optimality.

We compare the partition candidate pruning algorithm with the best existing optimization algorithms for multisplitting. For it the numbers of evaluated partition candidates are, on the average, only approximately 25% and 50% of those performed by the comparison methods. In time saving that amounts up to 50% less evaluation time per attribute.