Dimensionality reduction, classification, and spectral mixture analysis using non-negative underapproximation

Abstract

Non-negative matrix factorization (NMF) and its variants have recently been successfully used as dimensionality reduction techniques for identification of the materials present in hyperspectral images. We study a recently introduced variant of NMF called non-negative matrix underapproximation (NMU): it is based on the introduction of underapproximation constraints, which enables one to extract features in a recursive way, such as principal component analysis, but preserving non-negativity. We explain why these additional constraints make NMU particularly well suited to achieve a parts-based and sparse representation of the data, enabling it to recover the constitutive elements in hyperspectral images. Both ℓ2-norm and ℓ1-norm-based minimization of the energy functional are considered. We experimentally show the efficiency of this new strategy on hyperspectral images associated with space object material identification, and on HYDICE and related remote sensing images.