Unsupervised classification of hyperspectral images on spherical manifolds

Traditional statistical models for remote sensing data have mainly focused on the magnitude of feature vectors. To perform clustering with directional properties of feature vectors, other valid models need to be developed. Here we first describe the transformation of hyperspectral images onto a unit hyperspherical manifold using the recently proposed spherical local embedding approach. Spherical local embedding is a method that computes high-dimensional local neighborhood preserving coordinates of data on constant curvature manifolds. We then propose a novel von Mises-Fisher (vMF) distribution based approach for unsupervised classification of hyperspectral images on the established spherical manifold. A vMF distribution is a natural model for multivariate data on a unit hypersphere. Parameters for the model are estimated using the Expectation-Maximization procedure. A set of experimental results on modeling hyperspectral images as vMF mixture distributions demonstrate the advantages.