Nonlinear Mapping Based on Spectral Angle Preserving Principle for Hyperspectral Image Analysis

Abstract

The paper proposes three novel nonlinear dimensionality reduction methods for hyperspectral image analysis. The first two methods are based on the principle of preserving pairwise spectral angle mapper (SAM) measures for pixels in a hyperspectral image. The first method is derived in Cartesian coordinates, and the second one in hypersherical coordinates. The third method is based on the approximation of SAM measures by Euclidean distances. For the proposed methods, the paper provides both the theoretical background and fast numerical optimization algorithms based on the stochastic gradient descent technique. The experimental study of the proposed methods is conducted using publicly available hyperspectral images. The study compares the proposed nonlinear dimensionality reduction methods with the principal component analysis (PCA) technique that belongs to linear dimensionality reduction methods. The experimental results show that the proposed approaches provide higher classification accuracy compared to the linear technique when the nearest neighbor classifier using SAM measure is used for classification.