Efficient Sparse Low-Rank Tensor Completion Using the Frank-Wolfe Algorithm
Abstract
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 space-efficient 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.
Cite
Text
Guo et al. "Efficient Sparse Low-Rank Tensor Completion Using the Frank-Wolfe Algorithm." AAAI Conference on Artificial Intelligence, 2017. doi:10.1609/AAAI.V31I1.10886Markdown
[Guo et al. "Efficient Sparse Low-Rank Tensor Completion Using the Frank-Wolfe Algorithm." AAAI Conference on Artificial Intelligence, 2017.](https://mlanthology.org/aaai/2017/guo2017aaai-efficient-a/) doi:10.1609/AAAI.V31I1.10886BibTeX
@inproceedings{guo2017aaai-efficient-a,
title = {{Efficient Sparse Low-Rank Tensor Completion Using the Frank-Wolfe Algorithm}},
author = {Guo, Xiawei and Yao, Quanming and Kwok, James Tin-Yau},
booktitle = {AAAI Conference on Artificial Intelligence},
year = {2017},
pages = {1948-1954},
doi = {10.1609/AAAI.V31I1.10886},
url = {https://mlanthology.org/aaai/2017/guo2017aaai-efficient-a/}
}