A Scalable Approach to Modeling Nonlinear Structure inHyperspectral Imagery and Other High-Dimensional DataUsing Manifold Coordinate Representations

摘要

In the past we have presented a framework for deriving a set of intrinsic manifold coordinates that directly parameterizehigh-dimensional data, such as that found in hyperspectral imagery~(1234567 )~(10)In these previous works, we have describedthe potential utility of these representations for such diverse problems as land-cover mapping and in-water retrievals suchas bathymetry.~(10)Because the manifold coordinates are intrinsic, they offer the potential for significant compression ofthe data, and are furthermore very useful for displaying data structure that can not be seen by linear image processingrepresentations when the data is inherently nonlinear. This is especially true, for example, when the data are knownto contain strong nonlinearities, such as in the reflectance data obtained from hyperspectral imaging sensors over thewater, where the medium itself is attenuating~(235).~7These representations are also potentially useful in such applicationsas anomaly finding~2.~3A number of other researchers have looked at different aspects of the manifold coordinate represen-tations such as the best way to exploit these representations through the backend classifier,~(15)while others have examinedalternative manifold coordinate models.~(14)In this paper, we provide an overview of our scalable algorithm for derivingmanifold coordinate representations of high-dimensional data such as hyperspectral imagery, describe some of our recentwork to improve the local estimation of spectral neighborhood size, and demonstrate the benefits for problems such asanomaly finding.