Quantum mechanics

Algorithm

Norm (philosophy)

Pure mathematics

Regularization (linguistics)

Rank (graph theory)

Eigenvalues and eigenvectors

Computer science

Mathematical optimization

Tensor (intrinsic definition)

Physics

Singular value decomposition

Mathematics

Political science

Artificial intelligence

Combinatorics

Matrix norm

Singular value

In tensor completion tasks, the traditional low-rank tensor decomposition models suffer from the laborious model selection problem due to their high model sensitivity. In particular, for tensor ring (TR) decomposition, the number of model possibilities grows exponentially with the tensor order, which makes it rather challenging to find the optimal TR decomposition. In this paper, by exploiting the low-rank structure of the TR latent space, we propose a novel tensor completion method which is robust to model selection. In contrast to imposing the low-rank constraint on the data space, we introduce nuclear norm regularization on the latent TR factors, resulting in the optimization step using singular value decomposition (SVD) being performed at a much smaller scale. By leveraging the alternating direction method of multipliers (ADMM) scheme, the latent TR factors with optimal rank and the recovered tensor can be obtained simultaneously. Our proposed algorithm is shown to effectively alleviate the burden of TR-rank selection, thereby greatly reducing the computational cost. The extensive experimental results on both synthetic and real-world data demonstrate the superior performance and efficiency of the proposed approach against the state-of-the-art algorithms.

Tensor Ring Decomposition with Rank Minimization on Latent Space: An Efficient Approach for Tensor Completion