Randomization can also be beneficial for axis- parallel tree methods.
These methods search the space of all decision trees using random perturbations, additions and deletions of the splits. We believe that randomization is a powerful tool in the context of decision trees, and our experiments in Chapter 3 are just one example of how it might be exploited. It will be interesting to design algorithms to efficiently find splits which are more general than oblique splits, say, a class of hypercurves. However, caution must be exercised in such an effort. A main advantage of decision trees in particular, and hierarchical methods in general, is that they divide the classification problem into a sequence of subproblems which are, in principle, simpler to solve than the original problem.