TY - GEN
T1 - Guarantees of augmented trace norm models in tensor recovery
AU - Shi, Ziqiang
AU - Han, Jiqing
AU - Zheng, Tieran
AU - Li, Ji
PY - 2013
Y1 - 2013
N2 - This paper studies the recovery guarantees of the models of minimizing ∥Χ∥* + 1/2α ∥Χ∥ F2 where Χ is a tensor and ∥Χ∥* and ∥Χ∥ 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 ∥Χ∥* 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 Χ0, minimizing ∥Χ∥* + 1/2α ∥Χ∥ F2 returns the same solution as minimizing ∥Χ∥* almost whenever α ≥ 10 imax ∥X(i)0∥2.
AB - This paper studies the recovery guarantees of the models of minimizing ∥Χ∥* + 1/2α ∥Χ∥ F2 where Χ is a tensor and ∥Χ∥* and ∥Χ∥ 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 ∥Χ∥* 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 Χ0, minimizing ∥Χ∥* + 1/2α ∥Χ∥ F2 returns the same solution as minimizing ∥Χ∥* almost whenever α ≥ 10 imax ∥X(i)0∥2.
UR - https://www.scopus.com/pages/publications/84896063073
M3 - 会议稿件
AN - SCOPUS:84896063073
SN - 9781577356332
T3 - IJCAI International Joint Conference on Artificial Intelligence
SP - 1670
EP - 1676
BT - IJCAI 2013 - Proceedings of the 23rd International Joint Conference on Artificial Intelligence
T2 - 23rd International Joint Conference on Artificial Intelligence, IJCAI 2013
Y2 - 3 August 2013 through 9 August 2013
ER -