Discriminative directional classifiers

Abstract

In different areas of knowledge, phenomena are represented by directional-angular or periodic-data; from wind direction and geographical coordinates to time references like days of the week or months of the calendar. These values are usually represented in a linear scale, and restricted to a given range (e.g. [0,2 pi)), hiding the real nature of this information. Therefore, dealing with directional data requires special methods. So far, the design of classifiers for periodic variables adopts a generative approach based on the usage of the von Mises distribution or variants. Since for non-periodic variables state of the art approaches are based on non-generative methods, it is pertinent to investigate the suitability of other approaches for periodic variables. We propose a discriminative Directional Logistic Regression model able to deal with angular data, which does not make any assumption on the data distribution. Also, we study the expressiveness of this model for any number of features. Finally, we validate our model against the previously proposed directional naive Bayes approach and against a Support Vector Machine with a directional Radial Basis Function kernel with synthetic and real data obtaining competitive results.