Low-rank factorization for rank minimization with nonconvex regularizers

Rank minimization is of interest in machine learning applications such as recommender systems and robust principal component analysis. Minimizing the convex relaxation to rank problem, nuclear norm, an effective technique solve problem with strong performance guarantees. However, nonconvex relaxations have less estimation bias than norm can more accurately reduce effect noise on measurements. We develop efficient algorithms based iteratively reweighted schemes, while also utilizing low factorization for semidefinite programs put forth by Burer Monteiro. prove convergence computationally show advantages over alternating methods. Additionally, computational complexity each iteration our algorithm par other state art algorithms, allowing us quickly find solutions large matrices.