scholarly journals Stochastic Variance Reduced Multiplicative Update for Nonnegative Matrix Factorization

2018 ◽  
Author(s):  
Hiroyuki Kasai
Keyword(s):  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Multiplicative Update

scholarly journals Projected Gradient Methods for Nonnegative Matrix Factorization

2007 ◽  
Vol 19 (10) ◽  
pp. 2756-2779 ◽  
Author(s):  
Chih-Jen Lin
Keyword(s):  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Gradient Methods ◽  
Nonnegative Matrix ◽  
Theory And Practice ◽  
Bound Constraints ◽  
Projected Gradient ◽  
Matlab Code ◽  
Projected Gradient Methods ◽  
Multiplicative Update

Nonnegative matrix factorization (NMF) can be formulated as a minimization problem with bound constraints. Although bound-constrained optimization has been studied extensively in both theory and practice, so far no study has formally applied its techniques to NMF. In this letter, we propose two projected gradient methods for NMF, both of which exhibit strong optimization properties. We discuss efficient implementations and demonstrate that one of the proposed methods converges faster than the popular multiplicative update approach. A simple Matlab code is also provided.

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.

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