A two-phase rank-based algorithm for low-rank matrix completion

Matrix completion aims to recover an unknown low-rank matrix from a small subset of its entries. In many applications, the rank target is known in advance and this information can be useful process. paper, first, we revisit recently proposed rank-based heuristic for “known-rank” establish condition under which generated sequence quasi-Fejér convergent solution set. Then, by including acceleration mechanism similar Nesterov’s acceleration, obtain new heuristic. Even though convergence cannot granted general, it turns out that very as warm-start phase (phase one), providing suitable estimate regularization parameter good starting point accelerated proximal gradient algorithm two) aimed solve nuclear-norm regularized problem. Numerical experiments with both synthetic real data show resulting two-phase matrices, relatively high precision, faster than other well-established algorithms.