Structured Discriminative Nonnegative Matrix Factorization for hyperspectral unmixing

Hyperspectral unmixing is an important technique for identifying the constituent spectra and estimating their corresponding fractions in an image. Nonnegative Matrix Factorization (NMF) has recently been widely used for hyperspectral unmixing. However, due to the complex distribution of hyperspectral data, most existing NMF algorithms cannot adequately reflect the intrinsic relationship of the data. In this paper, we propose a novel method, Structured Discriminative Nonnegative Matrix Factorization (SDNMF), to preserve the structural information of hyperspectral data. This is achieved by introducing structured discriminative regularization terms to model both local affinity and distant repulsion of observed spectral responses. Moreover, considering that the abundances of most materials are sparse, a sparseness constraint is also introduced into SDNMF. Experimental results on both synthetic and real data have validated the effectiveness of the proposed method which achieves better unmixing performance than several alternative approaches.