The data set, shown in Figure , has 2000 instances in 2-D, each belonging to one of eight categories. This concept is difficult to learn for any axis-parallel method, for obvious reasons. It is also quite difficult for oblique methods, for several reasons. The effect of randomization in OC1. Results with LMDT and SADT are included for comparison after the four variants of OC1.
Size is average tree size measured by the number of leaf nodes.
The third column shows the average number of hyperplanes each algorithm considered while building one tree. The different results for OC1 were obtained by varying both the number of restarts and the number of random jumps. When random jumps were used, up to twenty random jumps were tried at each local minimum. As soon as one was found that improved the impurity of the current hyperplane, the algorithm moved the hyperplane and started running the deterministic perturbation procedure again. The trees were not pruned for any of the algorithms, because the data were noise-free and furthermore the emphasis was on search.