Rare categories abound and their characterization has heretofore received little attention. Fraudulent banking transactions, network intrusions, and rare diseases are examples of rare classes whose detection and characterization are of high value. However, accurate characterization is challenging due to high-skewness and non-separability from majority classes, e.g., fraudulent transactions masquerade as legitimate ones. This paper proposes the RACH algorithm by exploring the compactness property of the rare categories. It is based on an optimization framework which encloses the rare examples by a minimum-radius hyperball. The framework is then converted into a convex optimization problem, which is in turn effectively solved in its dual form by the projected subgradient method. RACH can be naturally kernelized. Experimental results validate the effectiveness of RACH.