Directional naive Bayes classifiers

Directional data are ubiquitous in science. These data have some special properties that rule out the use of classical statistics. Therefore, different distributions and statistics, such as the univariate von Mises and the multivariate von Mises–Fisher distributions, should be used to deal with this kind of information. We extend the naive Bayes classifier to the case where the conditional probability distributions of the predictive variables follow either of these distributions. We consider the simple scenario, where only directional predictive variables are used, and the hybrid case, where discrete, Gaussian and directional distributions are mixed. The classifier decision functions and their decision surfaces are studied at length. Artificial examples are used to illustrate the behavior of the classifiers. The proposed classifiers are then evaluated over eight datasets, showing competitive performances against other naive Bayes classifiers that use Gaussian distributions or discretization to manage directional data