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Nonnegative matrix factorization (NMF) and its numerous variants have been extensively studied and used in hyperspectral unmixing (HU). With the aid of the designed deep structure, deep NMF-based methods demonstrate advantages in exploring the hierarchical features of complex data. However, a noise corruption problem commonly exists in hyperspectral data and severely degrades the unmixing performance of deep NMF-based methods when applied to HU. In this study, we propose an ℓ 2 , 1 norm-based robust deep nonnegative matrix factorization ( ℓ 2 , 1 -RDNMF) for HU, which incorporates an ℓ 2 , 1 norm into the two stages of the deep structure to achieve robustness. The multiplicative updating rules of ℓ 2 , 1 -RDNMF are efficiently learned and provided. The efficiency of the presented method is verified in experiments using both synthetic and genuine data. [ABSTRACT FROM AUTHOR]