A note on depth-based classification of circular data

Abstract

A procedure is developed in order to deal with the classification problem of objects in circular statistics. It is fully non-parametric and based on depth functions for directional data. Using the so-called DD-plot, we apply the k-nearest neighbors method in order to discriminate between competing groups. Three different notions of data depth for directional data are considered: the angular simplicial, the angular Tukey and the arc distance. We investigate and compare their performances through the average misclassification rate with respect to different distributional settings by using simulated and real data sets. Results show that the use of the arc distance depth should be generally preferred, and in some cases it outperforms the classifier based both on the angular simplicial and Tukey depths.