Rare category analysis is of key importance both in theory and in practice. Previous research work focuses on supervised rare category analysis, such as rare category detection and rare category classification. In this paper, for the first time, we address the challenge of unsupervised rare category analysis, including feature selection and rare category selection. We propose to jointly deal with the two correlated tasks, so that they can benefit from each other. To this end, we design an optimization framework which is able to coselect the relevant features and the examples from the rare category (a.k.a. the minority class). It is well justified theoretically. Furthermore, we develop the Partial Augmented Lagrangian Method (PALM) to solve the optimization problem. Experimental results on both synthetic and real data sets show the effectiveness of the proposed method. © 2010 Wiley Periodicals, Inc. Statistical Analysis and Data Mining 3: 417-430, 2010.