On least squares rank minimization

Friday, March 30, 2012 - 10:00am - 10:45am
Keller 3-180
Xioatong Shen (University of Minnesota, Twin Cities)
In multivariate analysis, rank minimization emerges when a low-rank
structure of matrices is desired in addition to a small estimation error.
Rank minimization is nonconvex and generally NP-hard. In this talk,
I will present some of our recent results on rank minimization.
Computationally, we derive a closed-form for a
global minimizer of a nonconvex least squares problem, as well as
develop efficient algorithms to compute a global solution as well as an entire
regularization solution path. Theoretically, we show that our method
reconstructs the oracle estimator exactly for noisy data.
Finally, the utility of the proposed method is demonstrated by
simulations and image reconstruction from noisy background.

This work is joint with Shuo Xiang, Yunzhang Zhu and Jieping Ye.