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Linear Discriminant Analysis (LDA) is one of the oldest and most popularlinear methods for supervised classification problems. In this paper, wedemonstrate that it is possible to compute the exact projection vector from LDAmodels based on unlabelled data, if some minimal prior information isavailable. More precisely, we show that only one of the following three piecesof information is actually sufficient to compute the LDA projection vector ifonly unlabelled data are available: (1) the class average of one of the twoclasses, (2) the difference between both class averages (up to a scaling), or(3) the class covariance matrices (up to a scaling). These theoretical resultsare validated in numerical experiments, demonstrating that this minimallyinformed Linear Discriminant Analysis (MILDA) model closely matches theperformance of a supervised LDA model. Furthermore, we show that the MILDAprojection vector can be computed in a closed form with a computational costcomparable to LDA and is able to quickly adapt to non-stationary data, makingit well-suited to use as an adaptive classifier.

Minimally Informed Linear Discriminant Analysis: training an LDA model with unlabelled data