  Classification algorithms face difficulties when one or more classes have
limited training data. We are particularly interested in classification trees,
due to their interpretability and flexibility. When data are limited in one or
more of the classes, the estimated decision boundaries are often irregularly
shaped due to the limited sample size, leading to poor generalization error. We
propose a novel approach that penalizes the Surface-to-Volume Ratio (SVR) of
the decision set, obtaining a new class of SVR-Tree algorithms. We develop a
simple and computationally efficient implementation while proving estimation
consistency for SVR-Tree and rate of convergence for an idealized empirical
risk minimizer of SVR-Tree. SVR-Tree is compared with multiple algorithms that
are designed to deal with imbalance through real data applications.
