The problem of feature transformation arises in many fields of information processing, including machine learning, data compression, computer vision and geosciences applications. Here we discuss an approach that seeks a hyperspherical coordinate system preserving geodesic distances in the high dimensional hyperspectral data space. A lower dimensional hyperspherical manifold is computed using a lower rank matrix approximation algorithm combined with the recently proposed spherical embeddings method. Three spherical metrics for classification that exploits the nonlinear structure of hyperspectral imagery based on the properties of hyperspherical surfaces and their relationship with local tangent spaces are proposed. As part of experimental validation, results on modeling multi-class multispectral data using the proposed spherical geodesic nearest neighbor, the spherical Mahalanobis nearest neighbor and the spherical discriminant adaptive nearest neighbor rules are presented. The results indicate that the approach yields promising and better classification accuracies especially for difficult tasks in spaces with complex irregular class boundaries.
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