Non-convex low-rank matrix recovery with arbitrary outliers via median-truncated gradient descent
Abstract
Recent work has demonstrated the effectiveness of gradient descent for directly recovering the factors of low-rank matrices from random linear measurements in a globally convergent manner when initialized properly. However, the performance of existing algorithms is highly sensitive in the presence of outliers that may take arbitrary values. In this paper, we propose a truncated gradient descent algorithm to improve the robustness against outliers, where the truncation is performed to rule out the contributions of samples that deviate significantly from the sample median of measurement residuals adaptively in each iteration. We demonstrate that, when initialized in a basin of attraction close to the ground truth, the proposed algorithm converges to the ground truth at a linear rate for the Gaussian measurement model with a near-optimal number of measurements, even when a constant fraction of the measurements are arbitrarily corrupted. In addition, we propose a new truncated spectral method that ensures an initialization in the basin of attraction at slightly higher requirements. We finally provide numerical experiments to validate the superior performance of the proposed approach.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- May 07, 2019
- Source ID
- 10.1093/imaiai/iaz009
Entities
People
- Huishuai Zhang
- Yingbin Liang
- Yuanxin Li
- Yuejie Chi
Organizations
- Air Force Office of Scientific Research
- Army Research Office
- Carnegie Mellon University
- Microsoft Research Asia
- National Science Foundation
- Office of Naval Research
- Ohio State University