Exploiting manifold geometry in hyperspectral imagery

A new algorithm for exploiting the nonlinear structure of hyperspectral imagery is developed and compared against the de facto standard of linear mixing. This new approach seeks a manifold coordinate system that preserves geodesic distances in the high-dimensional hyperspectral data space. Algorithms for deriving manifold coordinates, such as isometric mapping (ISOMAP), have been developed for other applications. ISOMAP guarantees a globally optimal solution, but is computationally practical only for small datasets because of computational and memory requirements. Here, we develop a hybrid technique to circumvent ISOMAP´s computational cost. We divide the scene into a set of smaller tiles. The manifolds derived from the individual tiles are then aligned and stitched together to recomplete the scene. Several alignment methods are discussed. This hybrid approach exploits the fact that ISOMAP guarantees a globally optimal solution for each tile and the presumed similarity of the manifold structures derived from different tiles. Using land-cover classification of hyperspectral imagery in the Virginia Coast Reserve as a test case, we show that the new manifold representation provides better separation of spectrally similar classes than one of the standard linear mixing models. Additionally, we demonstrate that this technique provides a natural data compression scheme, which dramatically reduces the number of components needed to model hyperspectral data when compared with traditional methods such as the minimum noise fraction transform.