In this paper,we propose a decentralized algorithm to solve the low-rank matrix completion problem and analyze its privacy-preserving property.Suppose that we want to recover a low-rank matrix D=[D1,D2,・・・,DL]from a s...In this paper,we propose a decentralized algorithm to solve the low-rank matrix completion problem and analyze its privacy-preserving property.Suppose that we want to recover a low-rank matrix D=[D1,D2,・・・,DL]from a subset of its entries.In a network composed of L agents,each agent i observes some entries of Di.We factorize the unknown matrix D as the product of a public matrix X which is common to all agents and a private matrix Y=[Y1,Y2,・・・,YL]of which Yi is held by agent i only.Each agent i updates Yi and its local estimate of X,denoted by X(i),in an alternating manner.Through exchanging information with neighbors,all the agents move toward a consensus on the estimates X(i).Once the consensus is(nearly)reached throughout the network,each agent i recovers Di=X(i)Yi,thus D is recovered.In this progress,communication through the network may disclose sensitive information about the data matrices Di to a malicious agent.We prove that in the proposed algorithm,D-LMaFit,if the network topology is well designed,the malicious agent is unable to reconstruct the sensitive information from others.展开更多
文摘In this paper,we propose a decentralized algorithm to solve the low-rank matrix completion problem and analyze its privacy-preserving property.Suppose that we want to recover a low-rank matrix D=[D1,D2,・・・,DL]from a subset of its entries.In a network composed of L agents,each agent i observes some entries of Di.We factorize the unknown matrix D as the product of a public matrix X which is common to all agents and a private matrix Y=[Y1,Y2,・・・,YL]of which Yi is held by agent i only.Each agent i updates Yi and its local estimate of X,denoted by X(i),in an alternating manner.Through exchanging information with neighbors,all the agents move toward a consensus on the estimates X(i).Once the consensus is(nearly)reached throughout the network,each agent i recovers Di=X(i)Yi,thus D is recovered.In this progress,communication through the network may disclose sensitive information about the data matrices Di to a malicious agent.We prove that in the proposed algorithm,D-LMaFit,if the network topology is well designed,the malicious agent is unable to reconstruct the sensitive information from others.
