A Bayesian mixture model for clustering circular data

Abstract

Clustering complex circular phenomena is a common problem in different scientific disciplines. Examples include the clustering of directions of animal movement in the wild to identify migration patterns, and the classification of angular positions of meteorological events to investigate seasonality fluctuations. The main goal is to develop a novel methodology for clustering and classification of circular data, under a Bayesian mixture modeling framework. The mixture model is defined assuming that the number of components is finite, but unknown, and that each component follows a projected normal distribution. Model selection is performed by jointly making inferences about the parameters of the mixture model and the number of components, choosing the model with the highest posterior probability. A deterministic relabeling strategy is used to recover identifiability for the components in the chosen model. Estimates of both the posterior classification probabilities and the scaled densities are approximated via the relabeled MCMC output. The proposed methods are illustrated using both simulated and real datasets, and performance comparisons with existing strategies are also given. The results suggest that the new approach is an appealing alternative for the clustering and classification of circular data.