# Computing Singular Vectors with Random Noise

Tuesday, October 15, 2013 - 1:30pm - 2:30pm

Lind 305

Ke Wang (University of Minnesota, Twin Cities)

Computing 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, the data is usually perturbed by noise. The

following question is of importance: How much does the singular vector of

data matrix change under a small perturbation? The classical perturbation

results, i.e. Davis-Kahan theorem and Wedin sin theorem, give tight

estimates for the worst-case scenario. We show that better estimates can be

achieved if the data matrix is low rank and the perturbation is random.

This is joint work with Sean O'Rourke and Van Vu.

high dimensional data analysis with many applications in computer science

and statistics. In practice, the data is usually perturbed by noise. The

following question is of importance: How much does the singular vector of

data matrix change under a small perturbation? The classical perturbation

results, i.e. Davis-Kahan theorem and Wedin sin theorem, give tight

estimates for the worst-case scenario. We show that better estimates can be

achieved if the data matrix is low rank and the perturbation is random.

This is joint work with Sean O'Rourke and Van Vu.