Rank revealing‐based tensor completion using improved generalized tensor multi‐rank minimization

Abstract

Abstract The authors address the problem of tensor completion from limited samplings. An improved generalized tubal Kronecker decomposition is first proposed to reveal the tensor structure of the targeted data, and the improved generalized tensor tubal‐rank and multi‐rank are also introduced. The tensor completion problem is then formulated as the improved multi‐rank minimisation problem. Instead of using the singular value decomposition(SVD), this work proposes an alternating optimisation method to update all of the subspaces of the data tensor for the recovery process, and thus it is computationally inexpensive. A rank‐decreasing method is derived to reveal the tensor rank in order to avoid the troublesome user defined hyper‐parameter selection. Experiments are carried out on both the synthetic data and the real datasets, and it is shown that the proposed approach can get a better performance than the state‐of‐the‐art approaches with moderate computational complexity.

Keywords

• computational complexity
• concave programming
• matrix algebra
• minimisation
• optimisation
• singular value decomposition