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Nonnegative matrix factorization (NMF) has been recently applied to solve the hyperspectral unmixing problem because it ensures nonnegativity and needs no assumption for the presence of pure pixels. However, the algorithm has a large amount of local minima due to the obvious nonconvexity of the objective function. In order to improve its performance, auxiliary constraints can be introduced into the algorithm. In this paper, we propose a new approach named abundance separation and smoothness constrained NMF by introducing two constraints, namely, abundance separation and smoothness, into the NMF algorithm. These constraints are based on two properties of hyperspectral imagery. First, usually, every ground object presents dominance in a specific region of the entire image scene and the correlation is weak between different endmembers. Second, moving through various regions, ground objects usually vary slowly and abrupt changes rarely appear. We also propose a learning algorithm to further improve the performance of our method, from which the auxiliary constraints are removed at an appropriate time. The proposed algorithm retains all the advantages of NMF and effectively overcomes the shortcoming of local minima at the same time. Experimental results based on synthetic and real hyperspectral data show the superiority of the proposed algorithm with respect to other state-of-the-art approaches.