Traditionally, there are three species of classification: unsupervised,
supervised, and semi-supervised. Supervised and semi-supervised classification
differ by whether or not weight is given to unlabelled observations in the
classification procedure. In unsupervised classification, or clustering, all
observations are unlabeled and hence full weight is given to unlabelled
observations. When some observations are unlabelled, it can be very difficult
to \textit{a~priori} choose the optimal level of supervision, and the
consequences of a sub-optimal choice can be non-trivial. A flexible
fractionally-supervised approach to classification is introduced, where any
level of supervision --- ranging from unsupervised to supervised --- can be
attained. Our approach uses a weighted likelihood, wherein weights control the
relative role that labelled and unlabelled data have in building a classifier.
A comparison between our approach and the traditional species is presented
using simulated and real data. Gaussian mixture models are used as a vehicle to
illustrate our fractionally-supervised classification approach; however, it is
broadly applicable and variations on the postulated model can be easily made.
