An unsupervised clustering algorithm for data on the unit hypersphere

Directional data on a hypersphere has been used in biology, geology, medicine, meteorology and oceanography. Clustering is a useful tool for the analysis of these data on the unit hypersphere. In general, the EM algorithm with a mixture of von Mises distributions is the most commonly used clustering method for 2-dimensional directional data on the plane. However, the EM algorithm is sensitive to initialization, meaning the number of clusters needs to be assigned a priori. This study proposes an effectively unsupervised approach to clustering for these directional data on the unit hypersphere. The proposed clustering method is free of initialization. Without the need to assign the number of clusters, it becomes an unsupervised clustering method for the analysis of data on the unit hypersphere. Some numerical and real examples are given with comparisons to demonstrate the effectiveness and superiority of the proposed method. Finally, the proposed clustering algorithm is applied to cluster exoplanet data of extrasolar planets. The clustering results give the following important implications: (1) there are three major clusters and (2) stellar metallicity does not play a key role in exoplanet migration.