A Riemannian rank-adaptive method for low-rank matrix completion

The low-rank matrix completion problem can be solved by Riemannian optimization on a fixed-rank manifold. However, drawback of the known approaches is that rank parameter has to fixed priori. In this paper, we consider set bounded-rank matrices. We propose rank-adaptive method, which consists optimization, increase step and reduction step. explore its performance applied problem. Numerical experiments synthetic real-world datasets illustrate proposed method compares favorably with state-of-the-art algorithms. addition, it shows one incorporate each aspect framework separately into existing algorithms for purpose improving performance.