We present a novel method for unsupervised classification, including the discovery of a new category and precise object and part localization. Given a set of unlabelled images, some of which contain an object of an unknown category, with unknown location and unknown size relative to the background, the method automatically identifies the images that contain the objects, localizes them and their parts, and reliably learns their appearance and geometry for subsequent classification. Current unsupervised methods construct classifiers based on a fixed set of initial features. Instead, we propose a new approach which iteratively extracts new features and re-learns the induced classifier, improving class vs. non-class separation at each iteration. We develop two main tools that allow this iterative combined search. The first is a novel star-like model capable of learning a geometric class representation in the unsupervised setting. The second is learning of "part specific features"...