Unequal Priors in Linear Discriminant Analysis

摘要

Dealing with unequal priors in both linear discriminant analysis (LDA) based on Gaussian distribution (GDA) and in Fisher's linear discriminant analysis (FDA) is frequently used in practice but almost described in neither any textbook nor papers. This is one of the first papers exhibiting that GDA and FDA yield the same classification results for any number of classes and features. We discuss in which ways unequal priors have to enter these two methods in theory as well as algorithms. This may be of particular interest if prior knowledge is available and should be included in the discriminant rule. Various estimators that use prior probabilities in different places (e.g. prior-based weighting of the covariance matrix) are compared both in theory and by means of simulations.