Discriminant analysis is a technique for classifying a set of observations into pre-defined classes. The purpose is to determine the class of an observation based on a set of variables known as predictors or input variables. The model is built based on a set of observations for which the classes are known. This set of observations is sometimes referred to as the Training Set. Based on the Training Set, the technique constructs a set of linear functions of the predictors, known as discriminant functions, such that
L = b1x1 + b2x2 + ... + bnxn + c , where the Bs are discriminant coefficients, the Xs are the input variables or predictors, and C is a constant.
These discriminant functions are used to predict the class of a new observation with unknown class. For a k class problem, k discriminant functions are constructed. Given a new observation, all the k discriminant functions are evaluated, and the observation is assigned to class i if the ith discriminant function has the highest value.