A scalable approach to modeling nonlinear structure in hyperspectral imagery and other high-dimensional data using manifold coordinate representations

In the past we have presented a framework for deriving a set of intrinsic manifold coordinates that directly parameterize high-dimensional data, such as that found in hyperspectral imagery1234567.10 In these previous works, we have described the potential utility of these representations for such diverse problems as land-cover mapping and in-water retrievals such as bathymetry.10 Because the manifold coordinates are intrinsic, they offer the potential for significant compression of the data, and are furthermore very useful for displaying data structure that can not be seen by linear image processing representations when the data is inherently nonlinear. This is especially true, for example, when the data are known to contain strong nonlinearities, such as in the reflectance data obtained from hyperspectral imaging sensors over the water, where the medium itself is attenuating235.7 These representations are also potentially useful in such applications as anomaly finding2.3 A number of other researchers have looked at different aspects of the manifold coordinate representations such as the best way to exploit these representations through the backend classifier,15 while others have examined alternative manifold coordinate models.14 In this paper, we provide an overview of our scalable algorithm for deriving manifold coordinate representations of high-dimensional data such as hyperspectral imagery, describe some of our recent work to improve the local estimation of spectral neighborhood size, and demonstrate the benefits for problems such as anomaly finding.