SR-TCUR: Scalable and robust tubal CUR decomposition for large-scale multidimensional tensors

Tensor factorization techniques are valuable tools in the processing and analysis of large-scale data, such as images and videos, especially the CUR factorization methods, as they offer several advantages over other decompositions, such as interpretability and computational efficiency. Moreover, tensor decompositions based on the t-product concept have attracted much attention due to their success in various applications. This paper proposes a scalable and efficient tubal CUR decomposition method based on t-product, called SR-TCUR, that samples the significant lateral and horizontal slices based on the deterministic sampling method. SR-TCUR only requires observing and loading a few data samples into memory to construct the low-rank tensor approximation, making it scalable for large-scale data tensors. Various experiments on synthetic and real-world datasets with different dimensions and characteristics are conducted to evaluate the performance of the SR-TCUR method. The experimental results demonstrate that SR-TCUR outperforms the state-of-the-art methods of deterministic tensor CUR (TCUR) based on the t-product in computational complexity. It achieves an approximation accuracy close to the standard tensor CUR decomposition based on the tensor discrete empirical interpolation selection method, but with significant computational efficiency. Moreover, we utilize SR-TCUR to solve the tensor completion problem and recover the missing data entries. © 2025 Elsevier B.V.