  In supervised classification problems, the test set may contain data points
belonging to classes not observed in the learning phase. Moreover, the same
units in the test data may be measured on a set of additional variables
recorded at a subsequent stage with respect to when the learning sample was
collected. In this situation, the classifier built in the learning phase needs
to adapt to handle potential unknown classes and the extra dimensions. We
introduce a model-based discriminant approach, Dimension-Adaptive Mixture
Discriminant Analysis (D-AMDA), which can detect unobserved classes and adapt
to the increasing dimensionality. Model estimation is carried out via a full
inductive approach based on an EM algorithm. The method is then embedded in a
more general framework for adaptive variable selection and classification
suitable for data of large dimensions. A simulation study and an artificial
experiment related to classification of adulterated honey samples are used to
validate the ability of the proposed framework to deal with complex situations.
