Inexact block coordinate descent methods with application to non-negative matrix factorization

2011 ◽  
Vol 31 (4) ◽  
pp. 1431-1452 ◽  
Author(s):  
S. Bonettini
Keyword(s):  
Matrix Factorization ◽  
Coordinate Descent ◽  
Descent Methods ◽  
Block Coordinate Descent ◽  
Non Negative Matrix Factorization

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.

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 Iteration complexity analysis of block coordinate descent methods

2016 ◽  
Vol 163 (1-2) ◽  
pp. 85-114 ◽  
Author(s):  
Mingyi Hong ◽  
Xiangfeng Wang ◽  
Meisam Razaviyayn ◽  
Zhi-Quan Luo
Keyword(s):  
Complexity Analysis ◽  
Coordinate Descent ◽  
Descent Methods ◽  
Block Coordinate Descent ◽  
Iteration Complexity

scholarly journals Avoiding Communication in Primal and Dual Block Coordinate Descent Methods

2019 ◽  
Vol 41 (1) ◽  
pp. C1-C27 ◽  
Author(s):  
Aditya Devarakonda ◽  
Kimon Fountoulakis ◽  
James Demmel ◽  
Michael W. Mahoney
Keyword(s):  
Coordinate Descent ◽  
Descent Methods ◽  
Block Coordinate Descent ◽  
Primal And Dual
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