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Matrix Completion from Noisy Entries
matrix completion low-rank matrices spectral methods manifold optimization
2015/8/21
Given a matrix M of low-rank, we consider the problem of reconstructing it from noisy observations of a small, random subset of its entries. The problem arises in a variety of applications, from colla...
Let M be a random nα × n matrix of rank r ≪ n, and assume that a uniformly random subset E of its entries is observed. We describe an efficient algorithm that reconstructs M from |E| = O(r ...
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...
Realizability of Polytopes as a Low Rank Matrix Completion Problem
Realizability of Polytopes Low Rank Matrix Completion Problem
2011/2/22
Here we show that the problem of realizing a polytope with specified combinatorics is equivalent to a low rank matrix completion problem.This is comparable to known results reducing realizability to s...
Calibration for Ultrasound Breast Tomography Using Matrix Completion
Calibration Ultrasound Breast Tomography Matrix Completion
2011/3/3
We study the calibration problem in circular ultrasound tomography devices for breast imaging, where the sensor positions deviate from the circumference of a perfect circle.
Restricted strong convexity and weighted matrix completion: Optimal bounds with noise
Restricted strong convexity weighted matrix completion Optimal bounds with noise
2010/12/3
We consider the matrix completion problem under a form of row/column weighted entrywise sampling, including the case of uniform entrywise sampling as a special case.We analyze the associated random ob...
WEAKENING ASSUMPTIONS FOR DETERMINISTIC SUBEXPONENTIAL TIME NON-SINGULAR MATRIX COMPLETION
WEAKENING ASSUMPTIONS DETERMINISTIC NON-SINGULAR MATRIX
2012/11/30
Kabanets and Impagliazzo [9] show how to decide the circuit polynomial identity testing problem (CPIT) in deterministic subexponential time, assuming hardness of some explicit multilinear polynomial f...