Exact low-rank matrix completion via convex optimization

Suppose that one observes an incomplete subset of entries selected uniformly at random from a low-rank matrix. When is it possible to complete the matrix and recover the entries that have not been seen? We show that in very general settings, one can perfectly recover all of the missing entries from...

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Bibliographic Details
Published in2008 46th Annual Allerton Conference on Communication, Control, and Computing pp. 806 - 812
Main Authors Candes, E.J., Recht, B.
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.09.2008
Subjects
Compressed sensing
Covariance matrix
Image analysis
Information analysis
Mathematics
Matrix decomposition
Motion pictures
Programming profession
Scattering
Signal analysis
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ISBN1424429250
9781424429257
DOI10.1109/ALLERTON.2008.4797640

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Summary:Suppose that one observes an incomplete subset of entries selected uniformly at random from a low-rank matrix. When is it possible to complete the matrix and recover the entries that have not been seen? We show that in very general settings, one can perfectly recover all of the missing entries from a sufficiently large random subset by solving a convex programming problem. This program finds the matrix with the minimum nuclear norm agreeing with the observed entries. The techniques used in this analysis draw upon parallels in the field of compressed sensing, demonstrating that objects other than signals and images can be perfectly reconstructed from very limited information.
ISBN:1424429250
9781424429257
DOI:10.1109/ALLERTON.2008.4797640