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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...
HODGE METRIC COMPLETION OF THE TEICHM¨ ULLER SPACE OF CALABI–YAU MANIFOLDS
HODGE METRIC COMPLETION TEICHM¨ ULLER SPACE CALABI–YAU MANIFOLDS
2018/4/19
We prove that the Hodge metric completion of the Teichm¨uller space of polarized and marked Calabi–Yau manifolds is a complex affine manifold. We also show that the extended period map from the comple...
We extend the notion of exact completion on a weakly lex category to elementary doctrines. We show how any such doctrine admits an elementary quotient completion, which freely adds effective quotients...
The Metric Completion of Outer Space
The Metric Completion Outer Space the Lipschitz metric homeomorphic
2012/3/1
We prove that the completion of Outer Space with the Lipschitz metric is homeomorphic to the free splitting complex. We give a new proof of a theorem by Francaviglia and Martino [FMa] that the isometr...
Noise as a Boolean algebra of sigma-fields. I. Completion
Noise Boolean algebra of sigma-fields Probability
2011/9/9
Abstract: Nonclassical noises over the plane (such as the black noise of percolation) consist of sigma-fields corresponding to some planar domains. One can treat less regular domains as limits of more...
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...
Localisation and Completion with an addendum on the use of Brown-Peterson homology in stable homotopy
Localisation Completion addendum
2011/2/25
In spring 1973 Frank Adams gave a course at the University of Chicago on localisation and completion. This was in the very early days of the subject,which arose from disparate constructions of Quillen...
Complexity of minimize total weighted average completion time scheduling problems with release times
flow-shop scheduling problem transportation delays
2010/9/20
The paper considers the problem of scheduling n jobs in a two-machine flow-shop to minimize the weighted sum of completion times. Between the completion of an operation and the beginning of the next o...
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.
Singularities of the asymptotic completion of developable Möbius strips
developable Mö bius strips math
2010/11/18
We prove that the asymptotic completion of a developable M\"obius strip in Euclidean three-space must have at least one singular point other than cuspidal edge singularities. Moreover, if the strip co...