Spherical Nearest Neighbor Classification: Application to Hyperspectral Data

Abstract

The problem of feature transformation arises in many fields of information processing including machine learning, data compression, computer vision and geoscientific applications. In this paper, we investigate the transformation of hyperspectral data to a coordinate system that preserves geodesic distances on a constant curvature space. The transformation is performed using the recently proposed spherical embedding method. Based on the properties of hyperspherical surfaces and their relationship with local tangent spaces we propose three spherical nearest neighbor metrics for classification. 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 proposed metrics yields better classification accuracies especially for difficult tasks in spaces with complex irregular class boundaries. This promising outcome serves as a motivation for further development of new models to analyze hyperspectral images in spherical manifolds.