  Decision trees are a widely used method for classification, both by
themselves and as the building blocks of multiple different ensemble learning
methods. The Max-Cut decision tree involves novel modifications to a standard,
baseline model of classification decision tree construction, precisely CART
Gini. One modification involves an alternative splitting metric, maximum cut,
based on maximizing the distance between all pairs of observations belonging to
separate classes and separate sides of the threshold value. The other
modification is to select the decision feature from a linear combination of the
input features constructed using Principal Component Analysis (PCA) locally at
each node. Our experiments show that this node-based localized PCA with the
novel splitting modification can dramatically improve classification, while
also significantly decreasing computational time compared to the baseline
decision tree. Moreover, our results are most significant when evaluated on
data sets with higher dimensions, or more classes; which, for the example data
set CIFAR-100, enable a 49% improvement in accuracy while reducing CPU time by
94%. These introduced modifications dramatically advance the capabilities of
decision trees for difficult classification tasks.
