scholarly journals Nonnegative Matrix Factorization Based on Alternating Nonnegativity Constrained Least Squares and Active Set Method

2008 ◽  
Vol 30 (2) ◽  
pp. 713-730 ◽  
Author(s):  
Hyunsoo Kim ◽  
Haesun Park
Keyword(s):  
Least Squares ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Constrained Least Squares ◽  
Active Set ◽  
Active Set Method

scholarly journals An Inexact Update Method with Double Parameters for Nonnegative Matrix Factorization

2016 ◽  
Vol 2016 ◽  
pp. 1-6
Author(s):  
Xiangli Li ◽  
Wen Zhang ◽  
Xiaoliang Dong ◽  
Juanjuan Shi
Keyword(s):  
Matrix Factorization ◽  
Gradient Descent ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Optimal Solution ◽  
Active Set ◽  
Active Set Method ◽  
New Methods ◽  
Two Parameters ◽  
Multiplicative Update

Nonnegative matrix factorization (NMF) has been used as a powerful date representation tool in real world, because the nonnegativity of matrices is usually required. In recent years, many new methods are available to solve NMF in addition to multiplicative update algorithm, such as gradient descent algorithms, the active set method, and alternating nonnegative least squares (ANLS). In this paper, we propose an inexact update method, with two parameters, which can ensure that the objective function is always descent before the optimal solution is found. Experiment results show that the proposed method is effective.

scholarly journals Active Set Type Algorithms for Nonnegative Matrix Factorization in Hyperspectral Unmixing

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Li Sun ◽  
Congying Han ◽  
Ziwen Liu
Keyword(s):  
Matrix Factorization ◽  
Quadratic Convergence ◽  
Nonnegative Matrix Factorization ◽  
Computational Cost ◽  
Nonnegative Matrix ◽  
Image Mining ◽  
Active Set ◽  
Hyperspectral Unmixing ◽  
Numerical Tests ◽  
Sparse Features

Hyperspectral unmixing is a powerful method of the remote sensing image mining that identifies the constituent materials and estimates the corresponding fractions from the mixture. We consider the application of nonnegative matrix factorization (NMF) for the mining and analysis of spectral data. In this paper, we develop two effective active set type NMF algorithms for hyperspectral unmixing. Because the factor matrices used in unmixing have sparse features, the active set strategy helps reduce the computational cost. These active set type algorithms for NMF is based on an alternating nonnegative constrained least squares (ANLS) and achieve a quadratic convergence rate under the reasonable assumptions. Finally, numerical tests demonstrate that these algorithms work well and that the function values decrease faster than those obtained with other algorithms.

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