Endmember induction by lattice associative memories and multi-objective genetic algorithms

Abstract

Endmembers are the spectral signatures of the constituent materials of an scene captured with a hyperspectral sensor. Endmember induction algorithms (EIAs) try to extract the endmembers of the scene from the corresponding hyperspectral image. In this article, we benefit from recent theoretical results showing that a set of affine independent vectors can be extracted from the rows and columns of lattice autoassociative memories (LAAM). In the linear mixing model (LMM), endmembers are defined as the vertices of a convex polytope covering the data. Affine independence is a sufficient condition for a set of vectors to be the vertices of a convex polytope, and thus to be considered as endmembers. Our basic procedure is the WM algorithm extracting the endmembers from the dual LAAMs built to store the spectra of the hyperspectral image pixels. The set of endmembers induced by this algorithm defines a convex polytope covering the hyperspectral image data. However, the number of induced endmembers obtained by this procedure is too high for practical purposes, besides they are highly correlated. We apply a Multi-Objective Genetic Algorithm (MOGA) to the optimal selection of the image endmembers. Two fitness functions are used, the residual error of the unmixing process and the size of the set of endmembers. From the MOGA's Pareto front we decide the final set of endmembers by examining the decrease in residual error obtained by increasing the number of endmembers. We propose a faster MOGA where the error fitness function is replaced by a fitness function based on the correlation between endmembers. We compare our process with a state-of-the-art EIA on well known benchmark images. © 2012 Graña and Veganzones.