scholarly journals Realizability of Polytopes as a Low Rank Matrix Completion Problem

2014 ◽  
Vol 51 (4) ◽  
pp. 761-778 ◽  
Author(s):  
Michael Gene Dobbins
Keyword(s):  
Matrix Completion ◽  
Low Rank ◽  
Completion Problem ◽  
Rank Matrix ◽  
Matrix Completion Problem ◽  
Low Rank Matrix Completion ◽  
Low Rank Matrix

Matrix completion via minimizing an approximate rank

2019 ◽  
Vol 17 (05) ◽  
pp. 689-713
Author(s):  
Xueying Zeng ◽  
Lixin Shen ◽  
Yuesheng Xu ◽  
Jian Lu
Keyword(s):  
State Of The Art ◽  
Matrix Completion ◽  
Relaxation Parameter ◽  
Rank Function ◽  
Low Rank ◽  
Completion Problem ◽  
Rank Matrix ◽  
Matrix Completion Problem ◽  
Low Rank Matrix Completion ◽  
Low Rank Matrix

The low rank matrix completion problem which aims to recover a matrix from that having missing entries has received much attention in many fields such as image processing and machine learning. The rank of a matrix may be measured by the [Formula: see text] norm of the vector of its singular values. Due to the nonconvexity and discontinuity of the [Formula: see text] norm, solving the low rank matrix completion problem which is clearly NP hard suffers from computational challenges. In this paper, we propose a constrained matrix completion model in which a novel nonconvex continuous rank surrogate is used to approximate the rank function of a matrix, promote low rank of the recovered matrix and address the computational challenges. The proposed rank surrogate differs from the convex nuclear norm and other existing state-of-the-art nonconvex surrogates in a way that it alleviates the discontinuity and nonconvexity of the rank function through a local [Formula: see text]-relaxation of the [Formula: see text] norm so that it possesses several desirable properties. These properties ensure that it accurately approximates the rank function by choosing an appropriate relaxation parameter. We moreover develop an efficient iterative algorithm to solve the resulting model. We also propose strategies of automatically updating the relaxation parameter to practically ensure the global convergence and speed up the algorithm. We establish theoretical convergence results for the proposed algorithm. Experimental results are presented to demonstrate significant performance improvements of the proposed model and the associated algorithm as compared to state-of-the-art methods in both recoverability and computational efficiency.

scholarly journals A Riemannian rank-adaptive method for low-rank matrix completion

2021 ◽  
Author(s):  
Bin Gao ◽  
P.-A. Absil
Keyword(s):  
Matrix Completion ◽  
Adaptive Method ◽  
Low Rank ◽  
Riemannian Optimization ◽  
Completion Problem ◽  
Rank Matrix ◽  
Matrix Completion Problem ◽  
Fixed Rank ◽  
Low Rank Matrix Completion ◽  
Low Rank Matrix

AbstractThe low-rank matrix completion problem can be solved by Riemannian optimization on a fixed-rank manifold. However, a drawback of the known approaches is that the rank parameter has to be fixed a priori. In this paper, we consider the optimization problem on the set of bounded-rank matrices. We propose a Riemannian rank-adaptive method, which consists of fixed-rank optimization, rank increase step and rank reduction step. We explore its performance applied to the low-rank matrix completion problem. Numerical experiments on synthetic and real-world datasets illustrate that the proposed rank-adaptive method compares favorably with state-of-the-art algorithms. In addition, it shows that one can incorporate each aspect of this rank-adaptive framework separately into existing algorithms for the purpose of improving performance.

DOA Estimation for Antenna Array with Partially-Well Sensors via Low-Rank Matrix Completion

2013 ◽  
Vol 756-759 ◽  
pp. 3977-3981 ◽  
Author(s):  
Hua Xing Yu ◽  
Xiao Fei Zhang ◽  
Jian Feng Li ◽  
De Ben
Keyword(s):  
Missing Values ◽  
Linear Array ◽  
Matrix Completion ◽  
Doa Estimation ◽  
Low Rank ◽  
Uniform Linear Array ◽  
Completion Problem ◽  
Rank Matrix ◽  
Low Rank Matrix Completion ◽  
Low Rank Matrix

In this paper, we address the angle estimation problem in linear array with some ill sensors (partially-well sensors), which only work well randomly. The output of the array will miss some values, and this can be regarded as a low-rank matrix completion problem due to the property that the number of sources is smaller than the number of the total sensors. The output of the array, which is corrupted by the missing values and the noise, can be complete via the Optspace method, and then the angles can be estimated according to the complete output. The proposed algorithm works well for the array with some ill sensors; moreover, it is suitable for non-uniform linear array. Simulation results illustrate performance of the algorithm.

Unsupervised change detection of satellite images using low rank matrix completion

2013 ◽  
Vol 38 (23) ◽  
pp. 5146 ◽  
Author(s):  
Shibo Gao ◽  
Yongmei Cheng ◽  
Yongqiang Zhao
Keyword(s):  
Change Detection ◽  
Satellite Images ◽  
Matrix Completion ◽  
Low Rank ◽  
Rank Matrix ◽  
Low Rank Matrix Completion ◽  
Low Rank Matrix
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