Application of classification methods when group sizes are unequal by incorporation of prior probabilities to three common approaches: Application to simulations and mouse urinary chemosignals

Four common classification methods are described, Euclidean Distance to Centroids (EDC), Linear Discriminant Analysis (LDA), Quadratic Discriminant Analysis (QDA) and Support Vector Machines (SVM). In many applications of chemometrics e.g. in medicine and biology it is common for there to be unequal sample sizes in different groups. When class sizes are unequal the performance of some of these methods may be biased according to class size. This paper describes approaches for incorporating prior probabilities of class membership using Bayesian approaches to three of the methods LDA, QDA and SVM, either assuming equal probability or assuming that the relative sample sizes relate to the relative probabilities. EDC is used as a benchmark to determine model stabilities. The methods are illustrated by four simulated datasets of different structures and one real dataset consisting of the gas chromatographic profile of mouse urine comparing controls to those on a diet.