高维变形矩形矩阵及其在矩阵去噪中的应用
High dimensional deformed rectangular matrices with applications in matrix denoising
摘要：
我们考虑恢复一个低秩的$M \times N$矩阵$S$从它的噪声观测$\tilde{S}$在两个不同的制度。在$M$与$N$相当的假设下，我们提出了$S$的两个一致估计.我们的分析依赖于有限秩扰动的高维矩形矩阵的局部行为。我们还得到了这类矩阵的奇异值和向量的收敛极限和收敛速度。
英文摘要：
We consider the recovery of a low rank $M \times N$ matrix $S$ from its noisy observation $\tilde{S}$ in two different regimes. Under the assumption that $M$ is comparable to $N$, we propose two consistent estimators for $S$. Our analysis relies on the local behavior of the large dimensional rectangular matrices with finite rank perturbation. We also derive the convergent limits and rates for the singular values and vectors of such matrices.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
