Discriminant analysis algorithm based on a distance function and on a Bayesian decision

We propose a new algorithm for the allocation of an individual to one of several possible groups or populations. The algorithm enables us to define a finite partition over the sample space, based on distance function. This partition is used, jointly with the application of a standard Bayesian decision rule, to allocate individuals to the populations. The algorithm also provides a measure of the allocation confidence for each individual, in a similar manner to that of logistic regression. The error rates for classification are also computed using the leave-one-out method. Results are compared with those obtained with other discriminant analysis techniques previously reported: Fisher's linear discriminant function, the quadratic discriminant function, logistic discrimination, and others.