  Recently, there is a revival of interest in low-rank matrix completion-based
unsupervised learning through the lens of dual-graph regularization, which has
significantly improved the performance of multidisciplinary machine learning
tasks such as recommendation systems, genotype imputation and image inpainting.
While the dual-graph regularization contributes a major part of the success,
computational costly hyper-parameter tunning is usually involved. To circumvent
such a drawback and improve the completion performance, we propose a novel
Bayesian learning algorithm that automatically learns the hyper-parameters
associated with dual-graph regularization, and at the same time, guarantees the
low-rankness of matrix completion. Notably, a novel prior is devised to promote
the low-rankness of the matrix and encode the dual-graph information
simultaneously, which is more challenging than the single-graph counterpart. A
nontrivial conditional conjugacy between the proposed priors and likelihood
function is then explored such that an efficient algorithm is derived under
variational inference framework. Extensive experiments using synthetic and
real-world datasets demonstrate the state-of-the-art performance of the
proposed learning algorithm for various data analysis tasks.
