Despite the benefits deriving from explicitly modeling concept disjointness to increase the quality of the ontologies, the number of disjointness axioms in vocabularies for the Web of Data is still limited, thus risking to leave important constraints underspecified. Automated methods for discovering these axioms may represent a powerful modeling tool for knowledge engineers. For the purpose, we propose a machine learning solution that combines (unsupervised) distance-based clustering and the divide-and-conquer strategy. The resulting terminological cluster trees can be used to detect candidate disjointness axioms from emerging concept descriptions. A comparative empirical evaluation on different types of ontologies shows the feasibility and the effectiveness of the proposed solution that may be regarded as complementary to the current methods which require supervision or consider atomic concepts only.