Hyperspectral Intrinsic Dimensionality Estimation With Nearest-Neighbor Distance Ratios

Abstract

The first task to be performed in most hyperspectral unmixing chains is the estimation of the number of endmembers. Several techniques for this problem have already been proposed, but the class of fractal techniques for intrinsic dimensionality estimation is often overlooked. In this paper, we study an intrinsic dimensionality estimation technique based on the known scaling behavior of nearest-neighbor distance ratios, and its performance on the spectral unmixing problem. We present the relation between intrinsic manifold dimensionality and the number of endmembers in a mixing model, and investigate the effects of denoising and the statistics on the algorithm. The algorithm is compared with several alternative methods, such as Hysime, virtual dimensionality, and several fractal-dimension based techniques, on both artificial and real data sets. Robust behavior in the presence of noise, and independence of the spectral dimensionality, is demonstrated. Furthermore, due to its construction, the algorithm can be used for non-linear mixing models as well.