报告人：Chen Cheng (Peking University)
时间：2019-03-15 12:00-13:30
地点：Room 1560, Sciences Building No. 1
12:00-12:30 lunch；12:30-13:30 Talk
Abstract: In this talk, we study a curious phenomenon reflecting the interplay between asymmetry and the
spectral methods. Suppose we are interested in a rank-1 and symmetric matrix n-by-n matrix M*, yet only
a randomly perturbed version M is observed. The noise matrix M−M* is composed of independent and
zero-mean entries and is not symmetric. This might arise, for example, when we have two independent
samples for each entry of M* and arrange them into an asymmetric data matrix M. The aim is to estimate
the leading eigenvalue and eigenvector of M*. Somewhat unexpectedly, our findings reveal that the leading
eigenvalue of the data matrix M can be √n times more accurate than its leading singular value in eigenvalue
estimation. Further, the perturbation of any linear form of the leading eigenvector of M (e.g. entrywise
eigenvector perturbation) is provably well-controlled. We further provide partial theory for the more
general rank-r case; this allows us to accommodate the case when M* is rank-1 but asymmetric, by
considering eigen-decomposition of the associated rank-2 dilation matrix. The takeaway message is this:
arranging the data samples in an asymmetric manner and performing eigen-decomposition (as opposed to SVD) could sometimes be quite beneficial.
欢迎各位同学积极参加，报名链接https://www.wenjuan.com/s/jYnyu2A/， 报名截止时间为3月15日上午10:00，我们将为报名同学提供午餐。
