Variable selection and updating in model-based discriminant analysis for high dimensional data with food authenticity applications

Food authenticity studies are concerned with determining if food samples have been correctly labelled 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 datasets
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 datasets, our proposed
method outperformed default implementations of Random Forests, AdaBoost, transductive SVMs and Bayesian Multinomial Regression by substantial
margins.