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Title: A Note on Alternating Minimization Algorithm for the Matrix Completion Problem

Abstract

Here, 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.

Authors:
 [1]; ORCiD logo [2]
  1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
  2. 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):
LA-UR-16-23854
Journal ID: ISSN 1070-9908; TRN: US1702183
Grant/Contract Number:  
AC52-06NA25396; CMMI-1335155
Resource Type:
Accepted Manuscript
Journal Name:
IEEE Signal Processing Letters
Additional Journal Information:
Journal Volume: 23; Journal Issue: 10; Journal ID: ISSN 1070-9908
Publisher:
IEEE Signal Processing Society
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Mathematics; Alternating minimization; compressive sensing; low-rank 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 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.},
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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