Global centralised and structured discriminative non‐negative matrix factorisation for hyperspectral unmixing

Abstract

Advances have been achieved in hyperspectral unmixing using the existing manifold Non‐negative Matrix Factorisation methods, although most of these methods only exploit the preliminary structural information, that is, the nearest neighbour graph. Consequently, the performance of these methods would be degraded when considering only the geometrical structure due to the diverse distribution of the hyperspectral data, that is, the close pixels could belong to different categories or the distant points could be sampled from the same classes. In this context, the present study worked from the perspective of both global and local data relationships to develop and propose a novel approach—the Global centralised and Structured discriminative Non‐negative Matrix Factorisation (GSNMF)—to achieve a further effective representation of hyperspectral unmixing. GSNMF involved maintaining the global centralised clustering and the local structured discriminative regularisation, based on which it could perfectly mine the structure information and drive a discriminative representation of the data. Experiments comparing the application of GSNMF and the state‐of‐the‐art methods to synthetic data demonstrated the superiority of GSNMF. In addition, the consistency of the fractional abundances obtained using GSNMF with the real distributions of spectral data was evaluated on two real‐world datasets.