The Warmack-Gonzalez algorithm for linear two-category multivariable optimal discriminant analysis

For classification problems involving two categories and two or more attributes, multivariable optimal discriminant analysis (MultiODA) provides a linear function that maximizes classification accuracy in the training set (i.e., the set of data with which the function is determined). MultiODA is usually formulated as a mixed integer program and solved with a standard branch-and-bound code. Recent research has been frustrated by the inability to employ this procedure for problems involving samples with more than 100 observations, because of the prohibitive associated computational requirements. This paper describes an algorithm (WARMACK) that dramatically reduces the computer resources necessary to solve MultiODA problems, extends WARMACK to the more general weighted case, and illustrates WARMACK using applications in medicine, investment, and psychology. Monte Carlo research reveals that WARMACK offers greatest gains in solvable sample size when the number of attributes is small (e.g., four or less). Using WARMACK, MultiODA problems involving two classes, two attributes, and one thousand observations can be run in under three CPU minutes on an IBM 3090 mainframe computer.