Efficient Sparse Low-Rank Tensor Completion Using the Frank-Wolfe Algorithm

Most tensor problems are NP-hard, and low-rank tensor completion is much more difficult than low-rank matrix completion. In this paper, we propose a time and spaceefficient low-rank tensor completion algorithm by using the scaled latent nuclear norm for regularization and the Frank- Wolfe (FW) algorithm for optimization. We show that all the steps can be performed efficiently. In particular, FW’s linear subproblem has a closed-form solution which can be obtained from rank-one SVD. By utilizing sparsity of the observed tensor, we only need to maintain sparse tensors and a set of small basis matrices. Experimental results show that the proposed algorithm is more accurate, much faster and more scalable than the state-of-the-art.

Authors

• Xiawei Guo
• Quanming Yao Tsinghua university
• James Kwok

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