Sparse and low-rank decomposition for big data systems via smoothed Riemannian optimization

We provide a unified modeling framework of sparse and low-rank decomposition to investigate the fundamental limits of communication, computation, and storage in mobile big data systems. The resulting sparse and low-rank optimization problems are highly intractable non-convex optimization problems and conventional convex relaxation approaches are inapplicable, for which we propose a smoothed Riemannian optimization approach. We propose novel regularized formulations that allow to exploit the Riemannian geometry of fixed-rank matrices and induce sparsity in matrices. Empirical results show the speedup, scalability, and superior performance against state-of-art algorithms across different problem instances.