Student Seminars

Yiwei Zhang
PhD student, Department of Statistics, University of Michigan

Spectral Regularization Algorithms for Learning Corrupted Low-Rank Matrices

Robust principle component analysis attracted more and more attention recently. It is assumed that the data matrix is the superposition of a low rank component and a sparse component, in which case, a number of data points have a few arbitrarily corruptions. Recent work has considered another situation that entire data points are completely corrupted, leading to a row/column sparse component. To recover the low rank matrix and the element-wise or row/column sparse matrix, convex-optimization-based algorithms are generally applied. However, we notice that there is no systematic algorithm for the estimation, especially in the scenario with perturbation. We propose a series of spectral regularization algorithms for corrupted low rank matrices. The convergent results of the algorithms can be shown under certain conditions. It turns out that our algorithms are easy to implement and have less complexity. Numerical results support the applicability of our algorithms in practice.

Student Seminar Archive

For questions regarding the Statistics Student Seminar or if you are interested in presenting, please contact Joonha Park(joonhap@umich.edu) or Jingshen Wang(jshwang@umich.edu).