Work

Non-convex low-rank matrix recovery with arbitrary outliers via median-truncated gradient descent

Year: 2019

Type: article

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.

Source: Information and Inference A Journal of the IMA

DOI: 10.1093/imaiai/iaz009

Authors: Yuanxin Li, Yuejie Chi, Huishuai Zhang, Yingbin Liang

Institutions: Carnegie Mellon University, Microsoft Research Asia (China), The Ohio State University

Language: English

Topic: Sparse and Compressive Sensing Techniques

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green