<p>Non-negative Tucker decomposition (NTD) has received much attention due to its efficient processing of high-dimensional non-negative data. To preserve the intrinsic geometric structure of the data, various graph regularization NTD methods have been proposed. However, most existing methods rely on single graph regularization, limiting their flexibility and adaptability, since a single graph may not adequately capture the intrinsic manifold structure of various datasets. To address this problem, this paper introduces an auto-weighted multiple graph structure as the regularizer for NTD, and then proposes a novel method called auto-weighted multiple graph regularized non-negative Tucker decomposition (AMGRNTD). The AMGRNTD method utilizes a linear combination of multiple simple graphs to more effectively preserve the intrinsic manifold structure of the original data, offering greater applicability to practical problems than single graph-based methods. Furthermore, the AMGRNTD method automatically learns an optimal weight for each graph without additional parameters. Experimental results on four real-world datasets demonstrate that the proposed method achieves better performance in image clustering than some existing state-of-the-art graph-based regularization methods.</p>