  In many situations, classes of data points of primary interest also happen to
be those that are least numerous. A well-known example is detection of
fraudulent transactions among the collection of all financial transactions, the
vast majority of which are legitimate. These types of problems fall under the
label of `rare-category detection.' There are two challenging aspects of these
problems. The first is a general lack of labeled examples of the rare class and
the second is the potential non-separability of the rare class from the
majority (in terms of available features). Statistics related to the geometry
of the rare class (such as its intrinsic dimension) can be significantly
different from those for the majority class, reflecting the different dynamics
driving variation in the different classes. In this paper we present a new
supervised learning algorithm that uses a dimension-driven statistic, called
the kappa-profile, to classify whether unlabeled points belong to a rare class.
Our algorithm requires very few labeled examples and is invariant with respect
to translation so that it performs equivalently on both separable and
non-separable classes.
