scholarly journals On the nuclear norm heuristic for a Hankel matrix completion problem

Automatica ◽  
2015 ◽  
Vol 51 ◽  
pp. 268-272 ◽  
Author(s):  
Liang Dai ◽  
Kristiaan Pelckmans
Keyword(s):  
Matrix Completion ◽  
Hankel Matrix ◽  
Nuclear Norm ◽  
Completion Problem ◽  
Matrix Completion Problem

Nuclear norm and indicator function model for matrix completion

2016 ◽  
Vol 24 (1) ◽  
Author(s):  
Juan Geng ◽  
Laisheng Wang ◽  
Xiuyu Wang
Keyword(s):  
Proximal Point Algorithm ◽  
Matrix Completion ◽  
Indicator Function ◽  
Nuclear Norm ◽  
Proximal Point ◽  
Completion Problem ◽  
Matrix Completion Problem ◽  
The Matrix ◽  
Completion Problems ◽  
Norm Model

AbstractIn the matrix completion problem, most methods to solve the nuclear norm model are relaxing it to the nuclear norm regularized least squares problem. In this paper, we propose a new unconstraint model for matrix completion problem based on nuclear norm and indicator function and design a proximal point algorithm (PPA-IF) to solve it. Then the convergence of our algorithm is established strictly. Finally, we report numerical results for solving noiseless and noisy matrix completion problems and image reconstruction.

scholarly journals Medical Image Denoising Via Matrix Norm Minimization Problems

2021 ◽  
Vol 24 (2) ◽  
pp. 72-77
Author(s):  
Zainab Abd-Alzahra ◽  
◽  
Basad Al-Sarray ◽  
Keyword(s):  
Minimization Problem ◽  
Matrix Completion ◽  
Nuclear Norm ◽  
Nuclear Norm Minimization ◽  
Minimization Problems ◽  
Completion Problem ◽  
Norm Minimization ◽  
Matrix Completion Problem ◽  
The Matrix ◽  
The Given

This paper presents the matrix completion problem for image denoising. Three problems based on matrix norm are performing: Spectral norm minimization problem (SNP), Nuclear norm minimization problem (NNP), and Weighted nuclear norm minimization problem (WNNP). In general, images representing by a matrix this matrix contains the information of the image, some information is irrelevant or unfavorable, so to overcome this unwanted information in the image matrix, information completion is used to comperes the matrix and remove this unwanted information. The unwanted information is handled by defining {0,1}-operator under some threshold. Applying this operator on a given matrix keeps the important information in the image and removing the unwanted information by solving the matrix completion problem that is defined by P. The quadratic programming use to solve the given three norm-based minimization problems. To improve the optimal solution a weighted exponential is used to compute the weighted vector of spectral that use to improve the threshold of optimal low rank that getting from solving the nuclear norm and spectral norm problems. The result of applying the proposed method on different types of images is given by adopting some metrics. The results showed the ability of the given methods.

scholarly journals The Q-matrix completion problem

2009 ◽  
Vol 18 ◽  
Author(s):  
Luz DeAlba, ◽  
Leslie Hogben ◽  
Bhaba Sarma
Keyword(s):  
Matrix Completion ◽  
Completion Problem ◽  
Matrix Completion Problem ◽  
Q Matrix

scholarly journals A matrix completion problem over integral domains*: thecasewith 2n - 3 prescribed blocks *

2014 ◽  
Vol 33 (2) ◽  
pp. 215-233
Author(s):  
Alberto Borobia ◽  
Roberto Canogar ◽  
Helena Smigoc
Keyword(s):  
Matrix Completion ◽  
Integral Domains ◽  
Completion Problem ◽  
Matrix Completion Problem

scholarly journals The Q0-matrix completion problem

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Kalyan Sinha
Keyword(s):  
Matrix Completion ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Completion Problem ◽  
Matrix Completion Problem ◽  
Necessary And Sufficient ◽  
The Relationship

A matrix is a Q0-matrix if for every k∈{1,2,…,n}, the sum of all k×k principal minors is nonnegative. In this paper, we study some necessary and sufficient conditions for a digraph to have Q0-completion. Later on we discuss the relationship between Q and Q0-matrix completion problem. Finally, a classification of the digraphs of order up to four is done based on Q0-completion.

scholarly journals A matrix completion problem over integral domains: the case with 2n-3 prescribed entries

2010 ◽  
Vol 433 (3) ◽  
pp. 606-617 ◽  
Author(s):  
Alberto Borobia ◽  
Roberto Canogar ◽  
Helena Šmigoc
Keyword(s):  
Matrix Completion ◽  
Integral Domains ◽  
Completion Problem ◽  
Matrix Completion Problem

scholarly journals The Q1-matrix completion problem

2018 ◽  
Vol 06 (02) ◽  
pp. 443-450 ◽  
Author(s):  
Kalyan Sinha
Keyword(s):  
Matrix Completion ◽  
Completion Problem ◽  
Matrix Completion Problem

scholarly journals Nonlinear Traffic Prediction as a Matrix Completion Problem with Ensemble Learning

2021 ◽  
Author(s):  
Wenqing Li ◽  
Chuhan Yang ◽  
Saif Eddin Jabari
Keyword(s):  
High Resolution ◽  
Ensemble Learning ◽  
Operations Management ◽  
Matrix Completion ◽  
Traffic Prediction ◽  
Periodic Patterns ◽  
Data Set ◽  
Adaptive Boosting ◽  
Completion Problem ◽  
Matrix Completion Problem

This paper addresses the problem of short-term traffic prediction for signalized traffic operations management. Specifically, we focus on predicting sensor states in high-resolution (second-by-second). This contrasts with traditional traffic forecasting problems, which have focused on predicting aggregated traffic variables, typically over intervals that are no shorter than five minutes. Our contributions can be summarized as offering three insights: first, we show how the prediction problem can be modeled as a matrix completion problem. Second, we use a block-coordinate descent algorithm and demonstrate that the algorithm converges in sublinear time to a block coordinate-wise optimizer. This allows us to capitalize on the “bigness” of high-resolution data in a computationally feasible way. Third, we develop an ensemble learning (or adaptive boosting) approach to reduce the training error to within any arbitrary error threshold. The latter uses past days so that the boosting can be interpreted as capturing periodic patterns in the data. The performance of the proposed method is analyzed theoretically and tested empirically using both simulated data and a real-world high-resolution traffic data set from Abu Dhabi, United Arab Emirates. Our experimental results show that the proposed method outperforms other state-of-the-art algorithms.

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