A Note on Alternating Minimization Algorithm for the Matrix Completion Problem
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Gamarnik_A note on.pdf
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Author(s)
Gamarnik, David
Misra, Sidhant
Date Issued
June 2016
Journal
IEEE Signal Processing Letters
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Gamarnik, David and Misra, Sidhant. “A Note on Alternating Minimization Algorithm for the Matrix Completion Problem.” IEEE Signal Processing Letters 23, no. 10 (October 2016): 1340–1343. © 2016 Institute of Electrical and Electronics Engineers (IEEE)
Version
Original manuscript
Abstract
We consider the problem of reconstructing a low-rank matrix from a subset of its entries and analyze two variants of the so-called alternating minimization algorithm, which has been proposed in the past. We establish that when the underlying matrix has rank one, has positive bounded entries, and the graph underlying the revealed entries has diameter which is logarithmic in the size of the matrix, both algorithms succeed in reconstructing the matrix approximately in polynomial time starting from an arbitrary initialization. We further provide simulation results which suggest that the second variant which is based on the message passing type updates performs significantly better.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Sloan School of Management
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1109/LSP.2016.2576979
