Divide-and-Conquer Matrix Factorization

This work introduces SubMF, a parallel divide-and-conquer framework for noisy matrix factorization. SubMF divides a large-scale matrix factorization task into smaller subproblems, solves each subproblem in parallel using an arbitrary base matrix factorization algorithm, and combines the subproblem solutions using techniques from randomized matrix approximation. Our experiments with collaborative filtering, video background modeling, and simulated data demonstrate the near-linear to super-linear speed-ups attainable with this approach. Moreover, our analysis shows that SubMF enjoys high probability recovery guarantees comparable to those of its base algorithm.