Online Bayesian low-rank subspace learning from partial observations

Learning the underlying low-dimensional subspace from streaming incomplete high-dimensional observations data has attracted considerable attention lately. In this paper, we present a new computationally efficient Bayesian scheme for online low-rank subspace learning and matrix completion. The proposed scheme builds upon a properly defined hierarchical Bayesian model that explicitly imposes low rank to the latent subspace by assigning sparsity promoting Student-t priors to the columns of the subspace matrix. The new algorithm is fully automated and as corroborated by numerical simulations, provides higher estimation accuracy and a better estimate of the true subspace rank compared to state of the art methods.