Title: Random perturbation of low-rank matrices
Authors: Zhigang Bao - Hong Kong University of Science and Technology (Hong Kong)
Xiucai Ding - Duke University (United States)
Ke Wang - Hong Kong University of Science and Technology (Hong Kong) [presenting]
Abstract: Computing the singular values and singular vectors of a large matrix is a basic task in high dimensional data analysis with many applications in computer science and statistics. In practice, however, data is often perturbed by noise. We consider the matrix model $Y=S+X$ where $S$ is a low-rank deterministic matrix, representing the signal, and $X$ is random noise. We give a precise description of the limiting distribution of the angles between the outlier singular vectors of $Y$ with their counterparts, the leading singular vectors of $S$. It turns out that the limiting distribution depends on the structure of $S$ and the distribution of $X$, and thus it is non-universal.