1 research outputs found
Structured Low-Rank Matrix Factorization with Missing and Grossly Corrupted Observations
Recovering low-rank and sparse matrices from incomplete or corrupted
observations is an important problem in machine learning, statistics,
bioinformatics, computer vision, as well as signal and image processing. In
theory, this problem can be solved by the natural convex joint/mixed
relaxations (i.e., l_{1}-norm and trace norm) under certain conditions.
However, all current provable algorithms suffer from superlinear per-iteration
cost, which severely limits their applicability to large-scale problems. In
this paper, we propose a scalable, provable structured low-rank matrix
factorization method to recover low-rank and sparse matrices from missing and
grossly corrupted data, i.e., robust matrix completion (RMC) problems, or
incomplete and grossly corrupted measurements, i.e., compressive principal
component pursuit (CPCP) problems. Specifically, we first present two
small-scale matrix trace norm regularized bilinear structured factorization
models for RMC and CPCP problems, in which repetitively calculating SVD of a
large-scale matrix is replaced by updating two much smaller factor matrices.
Then, we apply the alternating direction method of multipliers (ADMM) to
efficiently solve the RMC problems. Finally, we provide the convergence
analysis of our algorithm, and extend it to address general CPCP problems.
Experimental results verified both the efficiency and effectiveness of our
method compared with the state-of-the-art methods.Comment: 28 pages, 9 figure