An Efficient Tensor Completion Method via New Latent Nuclear Norm
This work addresses tensor completion for applications like visual-data inpainting, offering improved efficiency for memory-limited equipment, but it is incremental as it builds on existing norm-based methods.
The paper tackles the problem of tensor completion by proposing a new latent nuclear norm with a balanced unfolding scheme to better capture global information, and develops an efficient method using the Frank-Wolfe algorithm that achieves state-of-the-art performance with reduced time and space costs, as demonstrated in visual-data inpainting experiments.
In tensor completion, the latent nuclear norm is commonly used to induce low-rank structure, while substantially failing to capture the global information due to the utilization of unbalanced unfolding scheme. To overcome this drawback, a new latent nuclear norm equipped with a more balanced unfolding scheme is defined for low-rank regularizer. Moreover, the new latent nuclear norm together with the Frank-Wolfe (FW) algorithm is developed as an efficient completion method by utilizing the sparsity structure of observed tensor. Specifically, both FW linear subproblem and line search only need to access the observed entries, by which we can instead maintain the sparse tensors and a set of small basis matrices during iteration. Most operations are based on sparse tensors, and the closed-form solution of FW linear subproblem can be obtained from rank-one SVD. We theoretically analyze the space-complexity and time-complexity of the proposed method, and show that it is much more efficient over other norm-based completion methods for higher-order tensors. Extensive experimental results of visual-data inpainting demonstrate that the proposed method is able to achieve state-of-the-art performance at smaller costs of time and space, which is very meaningful for the memory-limited equipment in practical applications.