Clustering Circular Data via Finite Mixtures of von Mises Distributions and an Application to Data on Wind Directions

The von Mises distribution, which is also known as the Circular Normal distribution is a well-studied and commonly used distribution for analyzing data on a unit circle. It has many properties and similarities to the normal distribution defined on the real line, making it popular for modeling circular data. Since it is unimodal, finite mixtures of von Mises distributions may be used to deal with circular data that may potentially have more than one mode. In this paper, our goal is to cluster such data sets after approximating each data set as a finite mixture of von Mises distributions. To accomplish such clustering we need a distance measure between any two such finite mixtures. For this, we propose using the Kullback-Liebler and Bhattacharyya distance measures. The applicability and usefulness of the proposed measures in identifying clusters present in a data set is first demonstrated through a simulation study. A real-life application that clusters the surface wind direction data in five major Indian cities is then studied using the proposed measures.