  Decision trees are a popular technique in statistical data classification.
They recursively partition the feature space into disjoint sub-regions until
each sub-region becomes homogeneous with respect to a particular class. The
basic Classification and Regression Tree (CART) algorithm partitions the
feature space using axis parallel splits. When the true decision boundaries are
not aligned with the feature axes, this approach can produce a complicated
boundary structure. Oblique decision trees use oblique decision boundaries to
potentially simplify the boundary structure. The major limitation of this
approach is that the tree induction algorithm is computationally expensive. In
this article we present a new decision tree algorithm, called HHCART. The
method utilizes a series of Householder matrices to reflect the training data
at each node during the tree construction. Each reflection is based on the
directions of the eigenvectors from each classes' covariance matrix.
Considering axis parallel splits in the reflected training data provides an
efficient way of finding oblique splits in the unreflected training data.
Experimental results show that the accuracy and size of the HHCART trees are
comparable with some benchmark methods in the literature. The appealing feature
of HHCART is that it can handle both qualitative and quantitative features in
the same oblique split.
