A Note on Alternating Minimization Algorithm for the Matrix Completion Problem

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...

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Bibliographic Details
Published in:IEEE signal processing letters Vol. 23; no. 10; pp. 1340 - 1343
Main Authors: Gamarnik, David, Misra, Sidhant
Format: Journal Article
Language:English
Published: New York IEEE 01.10.2016
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
IEEE Signal Processing Society
Subjects:
Algorithms
Alternating minimization
Approximation algorithms
Belief propagation
compressive sensing
Computer simulation
Graphs
low-rank matrix completion
Mathematics
MATHEMATICS AND COMPUTING
Message passing
Minimization
Optimization
Polynomials
Signal processing
Signal processing algorithms
Simulation
ISSN:1070-9908, 1558-2361
Online Access:Get full text
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Summary: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.
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USDOE Laboratory Directed Research and Development (LDRD) Program
AC52-06NA25396; CMMI-1335155
LA-UR-16-23854
National Science Foundation of China
ISSN:1070-9908
1558-2361
DOI:10.1109/LSP.2016.2576979