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Recently, sparse and low-rank graph-based discriminant analysis (SLGDA) has yielded satisfactory results in hyperspectral image (HSI) dimensionality reduction (DR), for which sparsity and low-rankness are simultaneously imposed to capture both local and global structure of hyperspectral data. However, SLGDA fails to exploit the spatial information. To address this problem, a tensor sparse and low-rank graph-based discriminant analysis (TSLGDA) is proposed in this paper. By regarding the hyperspectral data cube as a third-order tensor, small local patches centered at the training samples are extracted for the TSLGDA framework to maintain the structural information, resulting in a more discriminative graph. Subsequently, dimensionality reduction is performed on the tensorial training and testing samples to reduce data redundancy. Experimental results of three real-world hyperspectral datasets demonstrate that the proposed TSLGDA algorithm greatly improves the classification performance in the low-dimensional space when compared to state-of-the-art DR methods.