scholarly journals Support Recovery of Greedy Block Coordinate Descent Using the Near Orthogonality Property

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Haifeng Li
Keyword(s):  
Sparse Matrix ◽  
Coordinate Descent ◽  
Sufficient Condition ◽  
Block Coordinate Descent ◽  
Measurement Matrix ◽  
Orthogonality Property ◽  
Orthogonal Property ◽  
Support Recovery ◽  
Existing Result

In this paper, using the near orthogonal property, we analyze the performance of greedy block coordinate descent (GBCD) algorithm when both the measurements and the measurement matrix are perturbed by some errors. An improved sufficient condition is presented to guarantee that the support of the sparse matrix is recovered exactly. A counterexample is provided to show that GBCD fails. It improves the existing result. By experiments, we also point out that GBCD is robust under these perturbations.

scholarly journals Efficient Asynchronous Semi-stochastic Block Coordinate Descent Methods for Large-Scale SVD

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Fanhua Shang ◽  
Zhihui Zhang ◽  
Yuanyuan Liu ◽  
Hongying Liua ◽  
Jing Xu
Keyword(s):  
Large Scale ◽  
Coordinate Descent ◽  
Descent Methods ◽  
Block Coordinate Descent

scholarly journals A Block Coordinate Descent-Based Projected Gradient Algorithm for Orthogonal Non-Negative Matrix Factorization

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 540
Author(s):  
Soodabeh Asadi ◽  
Janez Povh
Keyword(s):  
Matrix Factorization ◽  
Synthetic Data ◽  
Coordinate Descent ◽  
The Other ◽  
Gradient Algorithm ◽  
Block Coordinate Descent ◽  
Projected Gradient Method ◽  
Projected Gradient ◽  
Factorization Problem ◽  
Non Negative Matrix Factorization

This article uses the projected gradient method (PG) for a non-negative matrix factorization problem (NMF), where one or both matrix factors must have orthonormal columns or rows. We penalize the orthonormality constraints and apply the PG method via a block coordinate descent approach. This means that at a certain time one matrix factor is fixed and the other is updated by moving along the steepest descent direction computed from the penalized objective function and projecting onto the space of non-negative matrices. Our method is tested on two sets of synthetic data for various values of penalty parameters. The performance is compared to the well-known multiplicative update (MU) method from Ding (2006), and with a modified global convergent variant of the MU algorithm recently proposed by Mirzal (2014). We provide extensive numerical results coupled with appropriate visualizations, which demonstrate that our method is very competitive and usually outperforms the other two methods.

Research on Compressed Sensing Matrix Based on Data Compressing of Insulator Leakage Current

2013 ◽  
Vol 475-476 ◽  
pp. 451-454
Author(s):  
Xue Ming Zhai ◽  
Xiao Bo You ◽  
Ruo Chen Li ◽  
Yu Jia Zhai ◽  
De Wen Wang
Keyword(s):  
Compressed Sensing ◽  
Data Compression ◽  
Leakage Current ◽  
Sparse Matrix ◽  
Circulant Matrix ◽  
Measurement Matrix ◽  
Sensing Matrix ◽  
Significant Step ◽  
On Line

Insulator fault may lead to the accident of power network,thus the on-line monitoring of insulator is very significant. Low rates wireless network is used for data transmission of leakage current. Making data compression and reconstruction of leakage current with the compressed sensing theory can achieve pretty good results. Determination of measurement matrix is the significant step for realizing the compressed sensing theory. This paper compares multiple measurement matrix of their effect via experiments, putting forward to make data compression and reconstruction of leakage current using Toeplitz matrix, circulant matrix and sparse matrix as measurement matrix, of which the reconstitution effect is almost the same as classical measurement matrix and depletes computational complexity and workload.

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