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Exact Matrix Completion via Convex Optimization
Matrix completion low-rank matrices convex optimization duality in optimization nuclear norm minimization random matrices noncommutative Khintchine inequality decoupling compressed sensing
2015/6/17
We consider a problem of considerable practical interest: the recovery of a data matrix from a sampling of its entries. Suppose that we observe m entries selected uniformly at random from a matrix M. ...
A SINGULAR VALUE THRESHOLDING ALGORITHM FOR MATRIX COMPLETION
Nuclear norm minimization matrix completion singular value thresholding Lagrange dual function Uzawa’s algorithm and linearized Bregman iteration
2015/6/17
This paper introduces a novel algorithm to approximate the matrix with minimum nuclear norm among all matrices obeying a set of convex constraints. This problem may be understood as the convex relaxat...
The Power of Convex Relaxation:Near-Optimal Matrix Completion
Matrix completion low-rank matrices semidefinite programming duality in optimization nuclear norm minimization random matrices and techniques from random matrix theory free probability
2015/6/17
This paper is concerned with the problem of recovering an unknown matrix from a small fraction of its entries. This is known as the matrix completion problem, and comes up in a great number of applica...
Matrix Completion with Noise
Matrix completion low-rank matrices semidefinite programming duality in optimization nuclear-norm minimization oracle inequalities compressed sensing
2015/6/17
On the heels of compressed sensing, a remarkable new field has very recently emerged. This field addresses a broad range of problems of significant practical interest, namely, the recovery of a data m...