@article{Qi2022, 
author = {Xinyu Qi and Jinru Wang and Jiating Shao},
title = {Minimax perturbation bounds of the low-rank matrix under Ky Fan norm},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {5},
pages = {7595-7605},
keywords = {singular value decomposition, Ky Fan norm, perturbation theory, sin Θ distance, low-rank matrix estimation},
url = {https://www.sciopen.com/article/10.3934/math.2022426},
doi = {10.3934/math.2022426},
abstract = {This paper considers the minimax perturbation bounds of the low-rank matrix under Ky Fan norm. We first explore the upper bounds via the best rank-   r approximation                      A        ^              r   of the observation matrix              A      ^      . Next, the lower bounds are established by constructing special matrix groups to show the upper bounds are tight on the low-rank matrix estimation error. In addition, we derive the rate-optimal perturbation bounds for the left and right singular subspaces under Ky Fan norm    sin  ⁡  Θ distance. Finally, some simulations have been carried out to support our theories.}
}