Authors: F. Shang (University of Hong Kong), Y. Liu (University of Hong Kong), J. Cheng (University of Hong Kong), H. Cheng (University of Hong Kong)
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Chapter Description
We propose a scalable Robust Bilinear Factorization (RBF) framework to recover low-rank and sparse matrices from incomplete, corrupted data or a small set of linear measurements. The proposed RBF framework not only takes into account the fact that the observations are contaminated by additive outliers and missing data, i.e., Robust Matrix Completion problems (RMC, i.e., RPCA plus LRMC), but can also identify both low-rank and sparse noisy components from incomplete and grossly corrupted measurements, i.e., CPCP problems.
In the unified RBF framework for both RMC and CPCP problems, repetitively calculating SVD of a large matrix is replaced by updating two much smaller factor matrices. By imposing the orthogonality constraint, the original RMC and CPCP problems are transformed into two smaller-scale matrix trace norm minimization problems. Moreover, we develop an efficient Alternating Direction Method of Multipliers (ADMM) to solve the RMC problem, and then extend it to solve CPCP problems.
Finally, we theoretically analyze the equivalent relationship between the QR scheme and the SVD scheme, and the convergence behavior of the proposed algorithms.