Presentation + Paper
24 August 2017 De-biasing low-rank projection for matrix completion
Simon Foucart, Deanna Needell, Yaniv Plan, Mary Wootters
Author Affiliations +
We study matrix completion with non-uniform, deterministic sampling patterns. We introduce a computable parameter, which is a function of the sampling pattern, and show that if this parameter is small, then we may recover missing entries of the matrix, with appropriate weights. We theoretically analyze a simple and well-known recovery method, which simply projects the (zero-padded) subsampled matrix onto the set of low-rank matrices. We show that under non-uniform deterministic sampling, this method yields a biased solution, and we propose an algorithm to de-bias it. Numerical simulations demonstrate that de-biasing significantly improves the estimate. However, when the observations are noisy, the error of this method can be sub-optimal when the sampling is highly non-uniform. To remedy this, we suggest an alternative which is based on projection onto the max-norm ball whose robustness to noise tolerates arbitrarily non-uniform sampling. Finally, we analyze convex optimization in this framework.
Conference Presentation
© (2017) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Simon Foucart, Deanna Needell, Yaniv Plan, and Mary Wootters "De-biasing low-rank projection for matrix completion", Proc. SPIE 10394, Wavelets and Sparsity XVII, 1039417 (24 August 2017); Logo
Cited by 6 scholarly publications.
Get copyright permission  Get copyright permission on Copyright Marketplace
Statistical analysis


Applied research in auditory data representation
Proceedings of SPIE (August 01 1990)
Diagnostics of stone samples by laser-induced flurorescence
Proceedings of SPIE (October 21 2004)
Design for manufacture with unknown tolerances
Proceedings of SPIE (September 12 2011)
Risk analysis on fabrication process of IRFPA
Proceedings of SPIE (September 08 2011)

Back to Top