Spectral Regularization Algorithms for Learning Corrupted Low-Rank Matrices

• Activity Number: 504
• Type: Contributed
• Date/Time: Wednesday, August 12, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Yiwei Zhang* and Ji Zhu
• Companies: University of Michigan and University of Michigan
• Keywords: Robust PCA ; corrupted matrices ; optimization

Abstract

Robust principle component analysis attracted much attention in recent years. 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 contain a few arbitrary corruptions. Recent work has also considered another situation in which 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, there is a lack of systematic algorithms for the estimation, especially in the scenario with perturbations. We propose a series of spectral regularization algorithms for denoising corrupted low rank matrices. Comparing with existing algorithms, the proposed algorithms are easy to implement and have less computational complexity. Convergence properties for the proposed algorithms can also be shown under certain conditions. Numerical results support the applicability of the proposed algorithms in practice.