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Hyperspectral unmixing is an essential research topic for spectral data analysis due to the existence of mixed pixels. Recently, many methods based on sparse nonnegative matrix factorization (NMF) have been widely used for unmixing by incorporating similarity preserving. However, most of them conduct the similarity learning and unmixing by using two separate steps, which may lead to the case that the learned similarity matrix is not the optimal one for unmixing. Thus, the performance of unmixing would be influenced and become undesirable. To alleviate this problem, we propose an adaptive relationship preserving-based sparse NMF (ARP-NMF) for hyperspectral unmixing. Typically, we regard similarity learning and unmixing as an alternative optimization process. During this process, the learned similarity weights and unmixing results can be mutually improved. Thus, our proposed method can learn the optimal similarity weights for unmixing and obtain better generalization ability for different hyperspectral images than traditional methods. Moreover, by using the spectral and spatial local structure, our ARP-NMF method effectively preserves structure consistency between pixels and abundances. Experimental results both on the synthetic data and the real data reveal that our proposed method outperforms several representative sparse NMF-based methods. [ABSTRACT FROM AUTHOR]