Scale-Space Clustering on a Unit Hypersphere

Abstract

We present an algorithm for the scale-space clustering of a point cloud on a hypersphere in a higher-imensional Euclidean space. Our method achieves clustering by estimating the density distribution of the points in the linear scale space on the sphere. The algorithm regards the union of observed point sets as an image defined by the delta functions located at the positions of the points on the sphere. As numerical examples, we illustrate clustering on the 3-sphere $\mathbb {S}^3$ in four-dimensional Euclidean space.