Guarantees of Augmented Trace Norm Models in Tensor Recovery

Abstract

This paper studies the recovery guarantees of the models of minimizing ||X|| ∗ + 1/2a ||X|| 2 F where X is a tensor and ||X|| ∗ and ||X|| F are the trace and Frobenius norm of respectively. We show that they can efficiently recover low-rank tensors. In particular, they enjoy exact guarantees similar to those known for minimizing ||X|| ∗ under the conditions on the sensing operator such as its null-space property, restricted isometry property, or spherical section property. To recover a low-rank tensor X 0 , minimizing ||X|| ∗ + 1/2a ||X|| 2 F returns the same solution as minimizing ||X|| ∗ almost whenever α ≥ 10max ||X 0 (i) || 2 .

Cite

Text

Shi et al. "Guarantees of Augmented Trace Norm Models in Tensor Recovery." International Joint Conference on Artificial Intelligence, 2013.

Markdown

[Shi et al. "Guarantees of Augmented Trace Norm Models in Tensor Recovery." International Joint Conference on Artificial Intelligence, 2013.](https://mlanthology.org/ijcai/2013/shi2013ijcai-guarantees/)

BibTeX

@inproceedings{shi2013ijcai-guarantees,
  title     = {{Guarantees of Augmented Trace Norm Models in Tensor Recovery}},
  author    = {Shi, Ziqiang and Han, Jiqing and Zheng, Tieran and Li, Ji},
  booktitle = {International Joint Conference on Artificial Intelligence},
  year      = {2013},
  pages     = {1670-1676},
  url       = {https://mlanthology.org/ijcai/2013/shi2013ijcai-guarantees/}
}