Modeling data manifold geometry in hyperspectral imagery

A new approach to modeling the nonlinear structure of hyperspectral imagery is developed. The new approach extracts a coordinate system that preserves geodesic distances on the high-dimensional data manifold. Extant algorithms for modelling nonlinear structure such as ISOMAP have been developed for other applications and are globally optimal but are practical only for small data sets because of poor computational scaling. We develop an approach to improve the scaling of manifold algorithms to large remote sensing scenes and illustrate our approach with hyperspectral imagery. We also show that the manifold approach leads to significantly improved compression over a widely used classical method, the minimum noise fraction