求解非负矩阵分解的子空间共轭梯度算法

›› 2014, Vol. 27 ›› Issue (1): 9-.

求解非负矩阵分解的子空间共轭梯度算法

孙良帅,李秀峰

(西安电子科技大学数学与统计学院,陕西西安 710071)

出版日期:2014-01-15 发布日期:2014-01-12
作者简介:孙良帅(1987—),男,硕士研究生。研究方向:最优化理论与方法,非负矩阵分解算法。E-mail:sunliangshuai_1987@163.com
基金资助:
中央高校基本科研业务费专项基金资助项目(K50513100007)

Solution to Non-Negative Matrix Factorization Subspace Conjugate Gradient Algorithm

SUN Liang-Shuai, LI Xiu-Feng

(School of Mathematics and Statistics,Xidian University,Xi'an 710071,China)

Online:2014-01-15 Published:2014-01-12

摘要/Abstract

摘要：

交替最小二乘法由于其理论可靠性和实际有效性成为非负矩阵分解中备受欢迎的方法之一。文中基于交替最小二乘法将界约束优化中的积极集共轭梯度法运用到非负矩阵分解当中,算法在子问题的求解中,并利用子空间的思想来划分指标集,并利用文献CHENG Wangyou文中的共轭梯度法进行变量更新,在一定条件下证明了新算法的收敛性,实验结果表明算法是有效的。

关键词: 非负矩阵分解, 交替最小二乘法, 共轭梯度法, 子空间

Abstract:

The alternating nonnegative least squares (ANLS),which is shown to be theoretically sound and empirically efficient,has been one of the most popular methods.Based on ANLS,this paper applies the active set conjugate gradient algorithm of bound constrained optimization to nonnegative matrix factorization.In solving subproblems,the index set is divided by employing the subspace strategy into four parts and then the conjugate gradient method proposed in ［13］ is used for updating the variables.The global convergence of the proposed algorithm is proved under mild conditions.Numerical experiments show the algorithm is efficient.

Key words: nonnegative matrix factorization;alternating nonnegative least squares method;conjugate gradient method;subspace

中图分类号:

孙良帅, 李秀峰. 求解非负矩阵分解的子空间共轭梯度算法[J]. , 2014, 27(1): 9-.

SUN Liang-Shuai, LI Xiu-Feng. Solution to Non-Negative Matrix Factorization Subspace Conjugate Gradient Algorithm[J]. , 2014, 27(1): 9-.

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