论文标题
schatten- $ q $低率矩阵扰动分析通过扰动投影错误绑定
A Schatten-$q$ Low-rank Matrix Perturbation Analysis via Perturbation Projection Error Bound
论文作者
论文摘要
本文研究了在扰动下通过奇异值分解的低级矩阵估计的schatten-q $误差。我们通过扰动投影误差绑定了在低级矩阵估计上绑定的扰动。然后，我们建立下限，以证明在低级矩阵估计误差上上限的紧密度。我们进一步开发了一个基于矩阵扰动投影错误绑定的用户友好的sin $θ$，用于单数子空间扰动。最后，我们证明了结果的优势，而不是通过模拟中的文献中的优势。
This paper studies the Schatten-$q$ error 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 sin$Θ$ 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.
