  Low-rank approximation models of data matrices have become important machine
learning and data mining tools in many fields including computer vision, text
mining, bioinformatics and many others. They allow for embedding
high-dimensional data into low-dimensional spaces, which mitigates the effects
of noise and uncovers latent relations. In order to make the learned
representations inherit the structures in the original data,
graph-regularization terms are often added to the loss function. However, the
prior graph construction often fails to reflect the true network connectivity
and the intrinsic relationships. In addition, many graph-regularized methods
fail to take the dual spaces into account. Probabilistic models are often used
to model the distribution of the representations, but most of previous methods
often assume that the hidden variables are independent and identically
distributed for simplicity. To this end, we propose a learnable
graph-regularization model for matrix decomposition (LGMD), which builds a
bridge between graph-regularized methods and probabilistic matrix decomposition
models. LGMD learns two graphical structures (i.e., two precision matrices) in
real-time in an iterative manner via sparse precision matrix estimation and is
more robust to noise and missing entries. Extensive numerical results and
comparison with competing methods demonstrate its effectiveness.
