Wavelet Filter Functions, the Matrix Completion Problem, and Projective Modules Over C ( T n )

2003 ◽  
Vol 9 (2) ◽  
pp. 101-116 ◽  
Author(s):  
Judith A. Packer ◽  
Marc A. Rieffel
Keyword(s):  
Matrix Completion ◽  
Projective Modules ◽  
Wavelet Filter ◽  
Completion Problem ◽  
Matrix Completion Problem ◽  
The Matrix

scholarly journals Speech Recognition: B

2021 ◽  
pp. 217-242
Author(s):  
Jean Walrand
Keyword(s):  
Matrix Completion ◽  
Gradient Projection ◽  
Stochastic Gradient ◽  
Projection Algorithm ◽  
General Technique ◽  
Gradient Projection Algorithm ◽  
Completion Problem ◽  
Matrix Completion Problem ◽  
Online Learning Algorithms ◽  
The Matrix

AbstractOnline learning algorithms update their estimates as additional observations are made. Section 12.1 explains a simple example: online linear regression. The stochastic gradient projection algorithm is a general technique to update estimates based on additional observations; it is widely used in machine learning. Section 12.2 presents the theory behind that algorithm. When analyzing large amounts of data, one faces the problems of identifying the most relevant data and of how to use efficiently the available data. Section 12.3 explains three examples of how these questions are addressed: the LASSO algorithm, compressed sensing, and the matrix completion problem. Section 12.4 discusses deep neural networks for which the stochastic gradient projection algorithm is easy to implement.

scholarly journals Enhancing Matrix Completion Using a Modified Second-Order Total Variation

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Wendong Wang ◽  
Jianjun Wang
Keyword(s):  
Total Variation ◽  
Optimization Problem ◽  
State Of The Art ◽  
Matrix Completion ◽  
Second Order ◽  
Low Rank ◽  
Superior Performance ◽  
Completion Problem ◽  
Matrix Completion Problem ◽  
The Matrix

In this paper, we propose a new method to deal with the matrix completion problem. Different from most existing matrix completion methods that only pursue the low rank of underlying matrices, the proposed method simultaneously optimizes their low rank and smoothness such that they mutually help each other and hence yield a better performance. In particular, the proposed method becomes very competitive with the introduction of a modified second-order total variation, even when it is compared with some recently emerged matrix completion methods that also combine the low rank and smoothness priors of matrices together. An efficient algorithm is developed to solve the induced optimization problem. The extensive experiments further confirm the superior performance of the proposed method over many state-of-the-art methods.

scholarly journals Drug-Target Interaction Prediction via Dual Laplacian Graph Regularized Matrix Completion

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Minhui Wang ◽  
Chang Tang ◽  
Jiajia Chen
Keyword(s):  
Drug Target ◽  
Chemical Structure ◽  
Genomic Sequence ◽  
Matrix Completion ◽  
Target Interaction ◽  
Interaction Prediction ◽  
Completion Problem ◽  
Matrix Completion Problem ◽  
The Matrix ◽  
Laplacian Graph

Drug-target interactions play an important role for biomedical drug discovery and development. However, it is expensive and time-consuming to accomplish this task by experimental determination. Therefore, developing computational techniques for drug-target interaction prediction is urgent and has practical significance. In this work, we propose an effective computational model of dual Laplacian graph regularized matrix completion, referred to as DLGRMC briefly, to infer the unknown drug-target interactions. Specifically, DLGRMC transforms the task of drug-target interaction prediction into a matrix completion problem, in which the potential interactions between drugs and targets can be obtained based on the prediction scores after the matrix completion procedure. In DLGRMC, the drug pairwise chemical structure similarities and the target pairwise genomic sequence similarities are fully exploited to serve the matrix completion by using a dual Laplacian graph regularization term; i.e., drugs with similar chemical structure are more likely to have interactions with similar targets and targets with similar genomic sequence similarity are more likely to have interactions with similar drugs. In addition, during the matrix completion process, an indicator matrix with binary values which indicates the indices of the observed drug-target interactions is deployed to preserve the experimental confirmed interactions. Furthermore, we develop an alternative iterative strategy to solve the constrained matrix completion problem based on Augmented Lagrange Multiplier algorithm. We evaluate DLGRMC on five benchmark datasets and the results show that DLGRMC outperforms several state-of-the-art approaches in terms of 10-fold cross validation based AUPR values and PR curves. In addition, case studies also demonstrate that DLGRMC can successfully predict most of the experimental validated drug-target interactions.

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.

On the matrix completion problem for multivariate filter bank construction

2007 ◽  
Vol 26 (1-3) ◽  
pp. 173-204 ◽  
Author(s):  
Qiuhui Chen ◽  
Charles A. Micchelli ◽  
Yuesheng Xu
Keyword(s):  
Filter Bank ◽  
Matrix Completion ◽  
Completion Problem ◽  
Matrix Completion Problem ◽  
The Matrix
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