Minimally Informed Linear Discriminant Analysis: training an LDA model
  with unlabelled data
Nicolas Heintz Tom Francart Alexander Bertrand
Linear Discriminant Analysis (LDA) is one of the oldest and most popular
linear methods for supervised classification problems. In this paper, we
demonstrate that it is possible to compute the exact projection vector from LDA
models based on unlabelled data, if some minimal prior information is
available. More precisely, we show that only one of the following three pieces
of information is actually sufficient to compute the LDA projection vector if
only unlabelled data are available: (1) the class average of one of the two
classes, (2) the difference between both class averages (up to a scaling), or
(3) the class covariance matrices (up to a scaling). These theoretical results
are validated in numerical experiments, demonstrating that this minimally
informed Linear Discriminant Analysis (MILDA) model closely matches the
performance of a supervised LDA model. Furthermore, we show that the MILDA
projection vector can be computed in a closed form with a computational cost
comparable to LDA and is able to quickly adapt to non-stationary data, making
it well-suited to use as an adaptive classifier.