Von Mises-Fisher Mean Shift for Clustering on a Hypersphere

We propose a method of clustering sample vectors on a hypersphere. Sample vectors are normalized in many cases, especially when applying kernel functions, and thus lie on a (unit) hypersphere. Considering the constraint of the hypersphere, the proposed method utilizes the von Mises-Fisher distribution in the framework of mean shift. It is also extended to the kernel-based clustering method via kernel tricks to cope with complex distributions. The algorithms of the proposed methods are based on simple matrix calculations. In the experiments, including a practical motion clustering task, the proposed methods produce favorable clustering results.