The minimum-rank gram matrix completion via modified fixed point continuation method
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Integrating low-rank and group-sparse structures for robust multi-task learning
Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining
Mining discriminative components with low-rank and sparsity constraints for face recognition
Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining
Low-rank Matrix Recovery via Iteratively Reweighted Least Squares Minimization
SIAM Journal on Optimization
Accelerated Linearized Bregman Method
Journal of Scientific Computing
Computing real solutions of polynomial systems via low-rank moment matrix completion
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
Iterative reweighted algorithms for matrix rank minimization
The Journal of Machine Learning Research
Matrix Recipes for Hard Thresholding Methods
Journal of Mathematical Imaging and Vision
A Simple Prior-Free Method for Non-rigid Structure-from-Motion Factorization
International Journal of Computer Vision
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The matrix rank minimization problem has applications in many fields, such as system identification, optimal control, low-dimensional embedding, etc. As this problem is NP-hard in general, its convex relaxation, the nuclear norm minimization problem, is often solved instead. Recently, Ma, Goldfarb and Chen proposed a fixed-point continuation algorithm for solving the nuclear norm minimization problem (Math. Program., doi: 10.1007/s10107-009-0306-5, 2009). By incorporating an approximate singular value decomposition technique in this algorithm, the solution to the matrix rank minimization problem is usually obtained. In this paper, we study the convergence/recoverability properties of the fixed-point continuation algorithm and its variants for matrix rank minimization. Heuristics for determining the rank of the matrix when its true rank is not known are also proposed. Some of these algorithms are closely related to greedy algorithms in compressed sensing. Numerical results for these algorithms for solving affinely constrained matrix rank minimization problems are reported.