TY - JOUR
T1 - Robust Inexact Alternating Optimization for Matrix Completion with Outliers
AU - Li , Ji
AU - Cai , Jian-Feng
AU - Zhao , Hongkai
JO - Journal of Computational Mathematics
VL - 2
SP - 337
EP - 354
PY - 2020
DA - 2020/02
SN - 38
DO - http://doi.org/10.4208/jcm.1809-m2018-0106
UR - https://global-sci.org/intro/article_detail/jcm/14520.html
KW - Matrix completion, ADMM, Outlier noise, Inexact projection.
AB - <p style="text-align: justify;">We investigate the problem of robust matrix completion with a fraction of observation corrupted by sparsity outlier noise. We propose an algorithmic framework based on the ADMM algorithm for a non-convex optimization, whose objective function consists of an $\ell_1$ norm data fidelity and a rank constraint. To reduce the computational cost per iteration, two inexact schemes are developed to replace the most time-consuming step in the generic ADMM algorithm. The resulting algorithms remarkably outperform the existing solvers for robust matrix completion with outlier noise. When the noise is severe and the underlying matrix is ill-conditioned, the proposed algorithms are faster and give more accurate solutions than state-of-the-art robust matrix completion approaches.</p>