  In this paper we present a new algorithm for learning oblique decision trees.
Most of the current decision tree algorithms rely on impurity measures to
assess the goodness of hyperplanes at each node while learning a decision tree
in a top-down fashion. These impurity measures do not properly capture the
geometric structures in the data. Motivated by this, our algorithm uses a
strategy to assess the hyperplanes in such a way that the geometric structure
in the data is taken into account. At each node of the decision tree, we find
the clustering hyperplanes for both the classes and use their angle bisectors
as the split rule at that node. We show through empirical studies that this
idea leads to small decision trees and better performance. We also present some
analysis to show that the angle bisectors of clustering hyperplanes that we use
as the split rules at each node, are solutions of an interesting optimization
problem and hence argue that this is a principled method of learning a decision
tree.
