TY - JOUR
T1 - Fast Low-Rank Bayesian Matrix Completion with Hierarchical Gaussian Prior Models
AU - Yang, Linxiao
AU - Fang, Jun
AU - Duan, Huiping
AU - Li, Hongbin
AU - Zeng, Bing
N1 - Publisher Copyright:
© 1991-2012 IEEE.
PY - 2018/6/1
Y1 - 2018/6/1
N2 - The problem of low-rank matrix completion is considered in this paper. To exploit the underlying low-rank structure of the data matrix, we propose a hierarchical Gaussian prior model, where columns of the low-rank matrix are assumed to follow a Gaussian distribution with zero mean and a common precision matrix, and a Wishart distribution is specified as a hyperprior over the precision matrix. We show that such a hierarchical Gaussian prior has the potential to encourage a low-rank solution. Based on the proposed hierarchical prior model, we develop a variational Bayesian matrix completion method, which embeds the generalized approximate massage passing technique to circumvent cumbersome matrix inverse operations. Simulation results show that our proposed method demonstrates superiority over some state-of-the-art matrix completion methods.
AB - The problem of low-rank matrix completion is considered in this paper. To exploit the underlying low-rank structure of the data matrix, we propose a hierarchical Gaussian prior model, where columns of the low-rank matrix are assumed to follow a Gaussian distribution with zero mean and a common precision matrix, and a Wishart distribution is specified as a hyperprior over the precision matrix. We show that such a hierarchical Gaussian prior has the potential to encourage a low-rank solution. Based on the proposed hierarchical prior model, we develop a variational Bayesian matrix completion method, which embeds the generalized approximate massage passing technique to circumvent cumbersome matrix inverse operations. Simulation results show that our proposed method demonstrates superiority over some state-of-the-art matrix completion methods.
KW - Matrix completion
KW - generalized approximate massage passing
KW - low-rank Bayesian learning
UR - http://www.scopus.com/inward/record.url?scp=85044069053&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85044069053&partnerID=8YFLogxK
U2 - 10.1109/TSP.2018.2816575
DO - 10.1109/TSP.2018.2816575
M3 - Article
AN - SCOPUS:85044069053
SN - 1053-587X
VL - 66
SP - 2804
EP - 2817
JO - IEEE Transactions on Signal Processing
JF - IEEE Transactions on Signal Processing
IS - 11
ER -