Learning-based EM clustering for data on the unit hypersphere with application to exoplanet data

This study focuses on clustering algorithms for data on the unit hypersphere. This type of directional data lain on the surface of a unit hypersphere is used in geology, biology, meteorology, medicine and oceanography. The EM algorithm with mixtures of von Mises-Fisher distributions is often used for model-based clustering for data on the unit hypersphere. However, the EM algorithm is sensitive to initial values and outliers and a number of clusters must be assigned a priori. In this paper, we propose an effective approach, called a learning-based EM algorithm with von Mises-Fisher distributions, to cluster this type of hyper-spherical data. The proposed clustering method is robust to outliers, without the need for initialization, and automatically determines the number of clusters. Thus, it becomes a fully-unsupervised model-based clustering method for data on the unit hypersphere. Some numerical and real examples with comparisons are given to demonstrate the effectiveness and superiority of the proposed method. We also apply the proposed learning-based EM algorithm to cluster exoplanet data in extrasolar planets. The clustering results have several important implications for exoplanet data and allow an interpretation of exoplanet migration. (C) 2017 Elsevier B.V. All rights reserved.