A Note on Alternating Minimization Algorithm for the Matrix Completion Problem
Abstract
Here, we consider the problem of reconstructing a lowrank matrix from a subset of its entries and analyze two variants of the socalled 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.
 Authors:

 Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Publication Date:
 Research Org.:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org.:
 USDOE Laboratory Directed Research and Development (LDRD) Program; National Science Foundation of China
 OSTI Identifier:
 1361478
 Report Number(s):
 LAUR1623854
Journal ID: ISSN 10709908; TRN: US1702183
 Grant/Contract Number:
 AC5206NA25396; CMMI1335155
 Resource Type:
 Accepted Manuscript
 Journal Name:
 IEEE Signal Processing Letters
 Additional Journal Information:
 Journal Volume: 23; Journal Issue: 10; Journal ID: ISSN 10709908
 Publisher:
 IEEE Signal Processing Society
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; Mathematics; Alternating minimization; compressive sensing; lowrank matrix completion
Citation Formats
Gamarnik, David, and Misra, Sidhant. A Note on Alternating Minimization Algorithm for the Matrix Completion Problem. United States: N. p., 2016.
Web. doi:10.1109/LSP.2016.2576979.
Gamarnik, David, & Misra, Sidhant. A Note on Alternating Minimization Algorithm for the Matrix Completion Problem. United States. doi:10.1109/LSP.2016.2576979.
Gamarnik, David, and Misra, Sidhant. Mon .
"A Note on Alternating Minimization Algorithm for the Matrix Completion Problem". United States. doi:10.1109/LSP.2016.2576979. https://www.osti.gov/servlets/purl/1361478.
@article{osti_1361478,
title = {A Note on Alternating Minimization Algorithm for the Matrix Completion Problem},
author = {Gamarnik, David and Misra, Sidhant},
abstractNote = {Here, we consider the problem of reconstructing a lowrank matrix from a subset of its entries and analyze two variants of the socalled 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.},
doi = {10.1109/LSP.2016.2576979},
journal = {IEEE Signal Processing Letters},
number = 10,
volume = 23,
place = {United States},
year = {2016},
month = {6}
}
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