The matrix-completion problem has attracted a lot of attention, largely as a
result of the celebrated Netflix competition. Two popular approaches for
solving the problem are nuclear-norm-regularized matrix approximation (Candes
and Tao, 2009, Mazumder, Hastie and Tibshirani, 2010), and maximum-margin
matrix factorization (Srebro, Rennie and Jaakkola, 2005). These two procedures
are in some cases
... [Show full abstract] solving equivalent problems, but with quite different
algorithms. In this article we bring the two approaches together, leading to an
efficient algorithm for large matrix factorization and completion that
outperforms both of these. We develop a software package "softImpute" in R for
implementing our approaches, and a distributed version for very large matrices
using the "Spark" cluster programming environment.