scholarly journals Fast Nonnegative Matrix Factorization: An Active-Set-Like Method and Comparisons

2011 ◽  
Vol 33 (6) ◽  
pp. 3261-3281 ◽  
Author(s):  
Jingu Kim ◽  
Haesun Park
Keyword(s):  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Active Set

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.

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 A Symmetric Rank-One Quasi-Newton Method for Nonnegative Matrix Factorization

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Shu-Zhen Lai ◽  
Hou-Biao Li ◽  
Zu-Tao Zhang
Keyword(s):  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Hessian Matrix ◽  
Synthetic Data ◽  
Nonnegative Matrix ◽  
Matrix Approximation ◽  
Active Set ◽  
Rank One ◽  
Symmetric Rank One ◽  
Quasi Newton

As is well known, the nonnegative matrix factorization (NMF) is a dimension reduction method that has been widely used in image processing, text compressing, signal processing, and so forth. In this paper, an algorithm on nonnegative matrix approximation is proposed. This method is mainly based on a relaxed active set and the quasi-Newton type algorithm, by using the symmetric rank-one and negative curvature direction technologies to approximate the Hessian matrix. The method improves some recent results. In addition, some numerical experiments are presented in the synthetic data, imaging processing, and text clustering. By comparing with the other six nonnegative matrix approximation methods, this method is more robust in almost all cases.

Sign in / Sign up

Export Citation Format

Share Document