TY - GEN
T1 - Decentralized low-rank matrix completion
AU - Ling, Qing
AU - Xu, Yangyang
AU - Yin, Wotao
AU - Wen, Zaiwen
PY - 2012
Y1 - 2012
N2 - This paper introduces algorithms for the decentralized low-rank matrix completion problem. Assume a low-rank matrix W = [W 1,W 2, ...,W L]. In a network, each agent ℓ observes some entries of W ℓ. In order to recover the unobserved entries of W via decentralized computation, we factorize the unknown matrix W as the product of a public matrix X, common to all agents, and a private matrix Y = [Y 1,Y 2, ...,Y L], where Y ℓ is held by agent ℓ. Each agent ℓ alternatively updates Y ℓ and its local estimate of X while communicating with its neighbors toward a consensus on the estimate. Once this consensus is (nearly) reached throughout the network, each agent ℓ recovers W ℓ = XY ℓ, and thus W is recovered. The communication cost is scalable to the number of agents, and W ℓ and Y ℓ are kept private to agent ℓ to a certain extent. The algorithm is accelerated by extrapolation and compares favorably to the centralized code in terms of recovery quality and robustness to rank over-estimate.
AB - This paper introduces algorithms for the decentralized low-rank matrix completion problem. Assume a low-rank matrix W = [W 1,W 2, ...,W L]. In a network, each agent ℓ observes some entries of W ℓ. In order to recover the unobserved entries of W via decentralized computation, we factorize the unknown matrix W as the product of a public matrix X, common to all agents, and a private matrix Y = [Y 1,Y 2, ...,Y L], where Y ℓ is held by agent ℓ. Each agent ℓ alternatively updates Y ℓ and its local estimate of X while communicating with its neighbors toward a consensus on the estimate. Once this consensus is (nearly) reached throughout the network, each agent ℓ recovers W ℓ = XY ℓ, and thus W is recovered. The communication cost is scalable to the number of agents, and W ℓ and Y ℓ are kept private to agent ℓ to a certain extent. The algorithm is accelerated by extrapolation and compares favorably to the centralized code in terms of recovery quality and robustness to rank over-estimate.
KW - decentralized algorithm
KW - low-rank matrix completion
KW - matrix factorization
KW - privacy protection
UR - http://www.scopus.com/inward/record.url?scp=84867595624&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84867595624&partnerID=8YFLogxK
U2 - 10.1109/ICASSP.2012.6288528
DO - 10.1109/ICASSP.2012.6288528
M3 - Conference contribution
AN - SCOPUS:84867595624
SN - 9781467300469
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - 2925
EP - 2928
BT - 2012 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2012 - Proceedings
T2 - 2012 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2012
Y2 - 25 March 2012 through 30 March 2012
ER -