Distributed nuclear norm minimization for matrix completion

Morteza Mardani, Gonzalo Mateos, Georgios B Giannakis

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations

Abstract

The ability to recover a low-rank matrix from a subset of its entries is the leitmotif of recent advances for localization of wireless sensors, unveiling traffic anomalies in backbone networks, and preference modeling for recommender systems. This paper develops a distributed algorithm for low-rank matrix completion over networks. While nuclear-norm minimization has well-documented merits when centralized processing is viable, the singular-value sum is non-separable and this challenges its minimization in a distributed fashion. To overcome this limitation, an alternative characterization of the nuclear norm is adopted which leads to a separable, yet non-convex cost that is minimized via the alternating-direction method of multipliers. The novel distributed iterations entail reduced-complexity per node tasks, and affordable message passing between single-hop neighbors. Interestingly, upon convergence the distributed (non-convex) estimator provably attains the global optimum of its centralized counterpart, regardless of initialization. Simulations corroborate the convergence of the novel distributed matrix completion algorithm, and its centralized performance guarantees.

Original languageEnglish (US)
Title of host publication2012 IEEE 13th International Workshop on Signal Processing Advances in Wireless Communications, SPAWC 2012
Pages354-358
Number of pages5
DOIs
StatePublished - Nov 2 2012
Event2012 IEEE 13th International Workshop on Signal Processing Advances in Wireless Communications, SPAWC 2012 - Cesme, Turkey
Duration: Jun 17 2012Jun 20 2012

Publication series

NameIEEE Workshop on Signal Processing Advances in Wireless Communications, SPAWC

Other

Other2012 IEEE 13th International Workshop on Signal Processing Advances in Wireless Communications, SPAWC 2012
Country/TerritoryTurkey
CityCesme
Period6/17/126/20/12

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