On Deterministic Sampling Patterns for Robust Low-Rank Matrix Completion

In this letter, we study the deterministic sampling patterns for the completion of low-rank matrix, when corrupted with a sparse noise, also known as robust matrix completion. We extend the recent results on the deterministic sampling patterns in the absence of noise based on the geometric analysis...

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Bibliographic Details
Published inIEEE signal processing letters Vol. 25; no. 3; pp. 343 - 347
Main Authors Ashraphijuo, Morteza, Aggarwal, Vaneet, Wang, Xiaodong
Format Journal Article
LanguageEnglish
Published IEEE 01.03.2018
Subjects
Deterministic guarantees
Electronic mail
Manifolds
Noise measurement
probabilistic guarantees
Probabilistic logic
robust matrix completion
Robustness
sampling pattern
Signal processing algorithms
Sparse matrices
sparse noise
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Summary:In this letter, we study the deterministic sampling patterns for the completion of low-rank matrix, when corrupted with a sparse noise, also known as robust matrix completion. We extend the recent results on the deterministic sampling patterns in the absence of noise based on the geometric analysis on the Grassmannian manifold. A special case where each column has a certain number of noisy entries is considered, where our probabilistic analysis performs very efficiently. Furthermore, assuming that the rank of the original matrix is not given, we provide an analysis to determine if the rank of a valid completion is indeed the actual rank of the data corrupted with sparse noise by verifying some conditions.
ISSN:1070-9908
1558-2361
DOI:10.1109/LSP.2017.2780983