Riemannian Perspective on Matrix Factorization

Matrix completion is a classical problem in machine learning and signal processing that aims to recover an unknown low-rank matrix from only a few observed entries. Ever since the pioneering work by Candès and Recht (2009), there have been a flurry of works solving matrix completion with guarantees. See a survey by Candès and Recht (2012) and the introduction of (Ge et al., 2016) for detailed information. Among many approaches, one prominent approach widely used in practice is based on matrix factorizations, à la Burer and Monteiro (2003).