Guarantees of Augmented Trace Norm Models in Tensor Recovery
Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence. Pages 1670-1675.
Abstract
This paper studies the recovery guarantees of the models of minimizing ||X||∗ + 1/2a ||X||2F 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 X0, minimizing ||X||∗ + 1/2a ||X||2F returns the same solution as minimizing ||X||∗ almost whenever α ≥ 10max ||X0(i)||2.
@inproceedings{ijcai2013p248,
title = {Guarantees of Augmented Trace Norm Models in Tensor Recovery},
author = {Shi, Ziqiang and Han, Jiqing and Zheng, Tieran and Li, Ji},
booktitle = {Proceedings of the Twenty-Third International Joint Conference on
Artificial Intelligence, {IJCAI-13}},
publisher = {AAAI Press / International Joint Conferences on Artificial Intelligence},
editor = {Francesca Rossi},
pages = {1670--1675},
year = {2013},
month = {8},
url = {https://ijcai.org/proceedings/2013/248},
}
TY - CPAPER TI - Guarantees of Augmented Trace Norm Models in Tensor Recovery AU - Shi, Ziqiang AU - Han, Jiqing AU - Zheng, Tieran AU - Li, Ji T2 - Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence, IJCAI-13 PB - AAAI Press / International Joint Conferences on Artificial Intelligence PY - 2013 SP - 1670 EP - 1675 UR - https://ijcai.org/proceedings/2013/248 ER -Copied
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