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 the rank minimization problem, the nuclear norm, is an effective technique to solve the problem with strong performance guarantees. However, nonconvex relaxations have less estimation bias than the nuclear norm and can more accurately reduce the effect of noise on the measurements. We develop efficient algorithms based on iteratively reweighted nuclear norm schemes, while also utilizing the low rank factorization for semidefinite programs put forth by Burer and Monteiro. We prove convergence and computationally show the advantages over convex relaxations and alternating minimization methods. Additionally, the computational complexity of each iteration of our algorithm is on par with other state of the art algorithms, allowing us to quickly find solutions to the rank minimization problem for large matrices.
Code (1)
Tasks
Recommendation SystemsSimilar Papers 제목 키워드 기반
Factor Group-Sparse Regularization for Efficient Low-Rank Matrix Recovery
This paper develops a new class of nonconvex regularizers for low-rank matrix recovery. Many regularizers are motivated as convex relaxations of the matrix rank function. Our new factor group-sparse regularizers are moti…
Low-Rank Matrix CompletionMatrix CompletionColumn $\ell_{2,0}$-norm regularized factorization model of low-rank matrix recovery and its computation
This paper is concerned with the column $\ell_{2,0}$-regularized factorization model of low-rank matrix recovery problems and its computation. The column $\ell_{2,0}$-norm of factor matrices is introduced to promote colu…
Matrix CompletionMulti-mode Core Tensor Factorization based Low-Rankness and Its Applications to Tensor Completion
Low-rank tensor completion has been widely used in computer vision and machine learning. This paper develops a novel multi-modal core tensor factorization (MCTF) method combined with a tensor low-rankness measure and a b…
DenoisingProvable Low Rank Plus Sparse Matrix Separation Via Nonconvex Regularizers
This paper considers a large class of problems where we seek to recover a low rank matrix and/or sparse vector from some set of measurements. While methods based on convex relaxations suffer from a (possibly large) estim…
Matrix CompletionLarge-Scale Low-Rank Matrix Learning with Nonconvex Regularizers
Low-rank modeling has many important applications in computer vision and machine learning. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has demonstrat…
Matrix Completion