On Fractionally-Supervised Classification: Weight Selection and Extension to the Multivariate t-Distribution

Abstract: Recent work on fractionally-supervised classification (FSC), an approach that allows classification to be carried out with a fractional amount of weight given to the unlabelled points, is further developed in two respects. The primary development addresses a question of fundamental importance over how to choose the amount of weight given to the unlabelled points. The resolution of this matter is essential because it makes FSC more readily applicable to real problems. Interestingly, the resolution of the weight selection problem opens up the possibility of a different approach to model selection in model-based clustering and classification. A secondary development demonstrates that the FSC approach can be effective beyond Gaussian mixture models. To this end, an FSC approach is illustrated using mixtures of multivariate t-distributions.