A Singular Value Thresholding Algorithm for Matrix Completion
SIAM Journal on Optimization
A novel framework based on trace norm minimization for audio event detection
ICONIP'11 Proceedings of the 18th international conference on Neural Information Processing - Volume Part II
Accelerated Linearized Bregman Method
Journal of Scientific Computing
Audio classification with low-rank matrix representation features
ACM Transactions on Intelligent Systems and Technology (TIST) - Special Section on Intelligent Mobile Knowledge Discovery and Management Systems and Special Issue on Social Web Mining
Approximation of rank function and its application to the nearest low-rank correlation matrix
Journal of Global Optimization
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The nuclear norm minimization problem is to find a matrix with the minimum nuclear norm subject to linear and second order cone constraints. Such a problem often arises from the convex relaxation of a rank minimization problem with noisy data, and arises in many fields of engineering and science. In this paper, we study inexact proximal point algorithms in the primal, dual and primal-dual forms for solving the nuclear norm minimization with linear equality and second order cone constraints. We design efficient implementations of these algorithms and present comprehensive convergence results. In particular, we investigate the performance of our proposed algorithms in which the inner sub-problems are approximately solved by the gradient projection method or the accelerated proximal gradient method. Our numerical results for solving randomly generated matrix completion problems and real matrix completion problems show that our algorithms perform favorably in comparison to several recently proposed state-of-the-art algorithms. Interestingly, our proposed algorithms are connected with other algorithms that have been studied in the literature.