TY - GEN
T1 - Distributed nuclear norm minimization for matrix completion
AU - Mardani, Morteza
AU - Mateos, Gonzalo
AU - Giannakis, Georgios B
PY - 2012/11/2
Y1 - 2012/11/2
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84868007917&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84868007917&partnerID=8YFLogxK
U2 - 10.1109/SPAWC.2012.6292926
DO - 10.1109/SPAWC.2012.6292926
M3 - Conference contribution
AN - SCOPUS:84868007917
SN - 9781467309714
T3 - IEEE Workshop on Signal Processing Advances in Wireless Communications, SPAWC
SP - 354
EP - 358
BT - 2012 IEEE 13th International Workshop on Signal Processing Advances in Wireless Communications, SPAWC 2012
T2 - 2012 IEEE 13th International Workshop on Signal Processing Advances in Wireless Communications, SPAWC 2012
Y2 - 17 June 2012 through 20 June 2012
ER -