Estimation of the Number of Endmembers in a Hyperspectral Image via the Hubness Phenomenon

Abstract

Estimation of the number of endmembers (NOE) is an important first step in many hyperspectral unmixing applications. We present a new method for solving this problem, based on the statistics of the indegree distribution (IDD) of the data nearest neighbor graph. It is known that this IDD shows a high dependence on the intrinsic dimensionality (ID) of the data, and becomes skewed for increasing dimensionality. This effect is known as the hubness phenomenon, and we propose a technique that exploits this effect to derive an estimate for the NOE in a hyperspectral data set. While this number should have a trivial relation with the ID of the data set, this relation is often obscured by the large correlations that exist between endmember spectra and adjacent spectral bands. The proposed technique circumvents this problem by building representative statistics based on simulated hyperspectral data sets, and therefore performs much better than alternative techniques. Also several types of nonlinearly mixed data sets can be treated by the proposed technique, which is illustrated with bilinear data sets.