Unsupervised Classification of Hyperspectral Images on Spherical Manifolds

Traditional statistical models for remote sensing data have mainly focused on data that is in Euclidean spaces. To perform clustering in non-Euclidean spaces, other models that are valid need to be developed. Here we first describe the transformation of hyperspectral images onto a unit hyperspherical manifold using the recently proposed spherical local embeddings approach. Spherical local embeddings is a method that computes high-dimensional local neighborhood preserving coordinates of data on constant curvature manifolds. We propose a lower rank matrix approximation algorithm to reduce the dimension of the embedded hyperspherical coordinates. A novel, von Mises-Fisher (vMF) distribution based approach for unsupervised classification of hyperspectral images on spherical manifolds is then presented. 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