In supervised learning, an important issue usually not taken into account by classical methods is the possibility of having in the test set individuals belonging to a class which has not been observed during the learning phase. Classical supervised algorithms will automatically label such observations as belonging to one of the known classes in the training set and will not be able to detect new classes. This work introduces a model-based discriminant analysis method, called adaptive mixture discriminant analysis (AMDA), which is able to detect unobserved groups of points and to adapt the learned classifier to the new situation. Two EM-based procedures are proposed for parameter estimation and Bayesian model selection is used for unobserved class detection. Experiments on artificial and real data demonstrate the ability of the proposed method to deal with complex and real word problems. The proposed approach is also applied to the detection of novel species in DNA barcoding.