We present a novel algorithm called Clicks, that finds clusters in categorical datasets based on a search for k-partite maximal cliques. Unlike previous methods, Clicks mines subspace clusters. It uses a selective vertical method to guarantee complete search. Clicks outperforms previous approaches by over an order of magnitude and scales better than any of the existing method for high-dimensional datasets. These results are demonstrated in a comprehensive performance study on real and synthetic datasets. Categories and Subject Descriptors: H.2.8 [Database Management]: Database Applications - Data Mining General Terms: Algorithms.