The proximity of an individual to a population with applications in discriminant analysis

We develop a proximity function between an individual and a population from a distance between multivariate observations. We study some properties of this construction and apply it to a distance-based discrimination rule, which contains the classic Linear discriminant function as a particular case. Additionally, this rule can be used advantageously for categorical or mixed variables, or in problems where a probabilistic model is not well determined. This approach is illustrated and compared with other classic procedures using four real data sets.