Unsupervised Classification of Hyperspectral Images on Spherical Manifolds
Abstract
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.
Date of this Version
12-20-2010