  Food authenticity studies are concerned with determining if food samples have
been correctly labeled or not. Discriminant analysis methods are an integral
part of the methodology for food authentication. Motivated by food authenticity
applications, a model-based discriminant analysis method that includes variable
selection is presented. The discriminant analysis model is fitted in a
semi-supervised manner using both labeled and unlabeled data. The method is
shown to give excellent classification performance on several high-dimensional
multiclass food authenticity data sets with more variables than observations.
The variables selected by the proposed method provide information about which
variables are meaningful for classification purposes. A headlong search
strategy for variable selection is shown to be efficient in terms of
computation and achieves excellent classification performance. In applications
to several food authenticity data sets, our proposed method outperformed
default implementations of Random Forests, AdaBoost, transductive SVMs and
Bayesian Multinomial Regression by substantial margins.
