A Schatten-q low-rank matrix perturbation analysis via perturbation projection error bound
A Schatten-q low-rank matrix perturbation analysis via perturbation projection error bound
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DOI：
10.1016/j.laa.2021.08.005
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发表时间：
2020-08
影响因子：
1.1
通讯作者：
Yuetian Luo;Rungang Han;Anru R. Zhang
中科院分区：
文献类型：
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作者：
Yuetian Luo;Rungang Han;Anru R. Zhang
本文研究了低秩矩阵奇异值分解估计在扰动下的Schatten-q误差。我们通过扰动投影误差界建立了低秩矩阵估计的扰动界。然后，我们建立下界来证明低秩矩阵估计误差上界的严密性。基于矩阵扰动投影误差界，我们进一步给出了奇异子空间扰动的sinΘ界.最后，我们通过模拟证明了我们的结果比文献中的结果的优势。
This paper studies the Schatten-qerror of low-rank matrix estimation by singular value decomposition under perturbation. We specifically establish a perturbation bound on the low-rank matrix estimation via a perturbation projection error bound. Then, we establish lower bounds to justify the tightness of the upper bound on the low-rank matrix estimation error. We further develop a user-friendly sinΘ bound for singular subspace perturbation based on the matrix perturbation projection error bound. Finally, we demonstrate the advantage of our results over the ones in the literature by simulation.