Functional clustering on a sphere via Riemannian functional principal components

Abstract

We propose the functional clustering algorithm applicable to the sphere-valued random curves, called k-centres Riemannian functional clustering (kCRFC). It is based on Riemannian functional principal component scores and k-centres functional clustering algorithm, thus we can obtain accurate clustering results by reflecting the geometry of the sphere. Our method shows better clustering performances than existing multivariate functional clustering methods in various simulation settings. We apply the proposed method to the migration trajectories of Egyptian Vultures in the Middle East and East Africa, and fruit fly behaviors, containing the curves lied on two dimensional and three dimensional sphere, respectively.