  We use a geometric digraph family called class cover catch digraphs (CCCDs)
to tackle the class imbalance problem in statistical classification. CCCDs
provide graph theoretic solutions to the class cover problem and have been
employed in classification. We assess the classification performance of CCCD
classifiers by extensive Monte Carlo simulations, comparing them with other
classifiers commonly used in the literature. In particular, we show that CCCD
classifiers perform relatively well when one class is more frequent than the
other in a two-class setting, an example of the class imbalance problem. We
also point out the relationship between class imbalance and class overlapping
problems, and their influence on the performance of CCCD classifiers and other
classification methods as well as some state-of-the-art algorithms which are
robust to class imbalance by construction. Experiments on both simulated and
real data sets indicate that CCCD classifiers are robust to the class imbalance
problem. CCCDs substantially undersample from the majority class while
preserving the information on the discarded points during the undersampling
process. Many state-of-the-art methods, however, keep this information by means
of ensemble classifiers, but CCCDs yield only a single classifier with the same
property, making it both appealing and fast.
