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Proceedings Paper

De-biasing low-rank projection for matrix completion
Author(s): Simon Foucart; Deanna Needell; Yaniv Plan; Mary Wootters
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Paper Abstract

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.

Paper Details

Date Published: 24 August 2017
PDF: 13 pages
Proc. SPIE 10394, Wavelets and Sparsity XVII, 1039417 (24 August 2017); doi: 10.1117/12.2275004
Show Author Affiliations
Simon Foucart, Texas A&M Univ. (United States)
Deanna Needell, Univ. of California, Los Angeles (United States)
Yaniv Plan, The Univ. of British Columbia (Canada)
Mary Wootters, Stanford Univ. (United States)


Published in SPIE Proceedings Vol. 10394:
Wavelets and Sparsity XVII
Yue M. Lu; Dimitri Van De Ville; Manos Papadakis, Editor(s)

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