计算机工程 ›› 2019, Vol. 45 ›› Issue (2): 220-225,232.doi: 10.19678/j.issn.1000-3428.0049293

• 图形图像处理 • 上一篇    下一篇

基于邻近交替线性化的稀疏非负矩阵分解算法

王静a,杨丹a,b   

  1. 重庆大学 a.数学与统计学院; b.软件学院 重庆401331
  • 收稿日期:2017-11-13 出版日期:2019-02-15 发布日期:2019-02-15
  • 作者简介:王静(1993—),女,硕士研究生,主研方向为计算机视觉、机器学习;杨丹,教授、博士生导师。
  • 基金项目:

    国家自然科学基金(61173131);中央高校基本科研业务费跨学科类重大项目(CDJZR12098801)。

Sparse Non-negative Matrix Factorization Algorithm Based on Proximal Alternating Linearized Minimization

WANG Jing a,YANG Dan a,b   

  1. a.College of Mathematics and Statistics; b.School of Software Engineering,Chongqing University,Chongqing 401331,China
  • Received:2017-11-13 Online:2019-02-15 Published:2019-02-15

摘要:

结合稀疏约束与邻近交替线性化(PALM),提出稀疏非负矩阵分解算法(SNMF_PALM)。将非凸的平滑剪切绝对偏差函数作为稀疏正则项,获得逼近L0范数的最佳凸松弛,并利用PALM算法对非凸问题进行求解,得到SNMF_PALM算法的局部稳定最优解。在人脸数据库上将SNMF_PALM算法与SNMF、NMF算法进行实验对比,结果表明SNMF_PALM算法具有更好的聚类性能。

关键词: 非负矩阵分解, 稀疏, 平滑剪切绝对偏差函数, 邻近交替线性化, 非凸问题, 聚类

Abstract:

This paper combinessparsity constraint and Proximal Alternating Linearized Minimization(PALM),proposes a Sparse Non-negative Matrix Factorization(SNMF) algorithm,called SNMF_PALM.The non-convex Smoothly Clipped Absolute Deviation(SCAD) function is used as the sparse regularization term to obtain the optimal convex relaxation approximating L0 norm.The PALM algorithm is used to solve the non-convex problem,and the local optimal solution of SNMF_PALM algorithm is obtained.Experimental results of SNMF_PALM,SNMF and improved NMF algorithms in face database show that SNMF_PALM algorithm has better clustering performance.

Key words: Non-negative Matrix Factorization(NMF), sparse, Smoothly Clipped Absolute Deviation(SCAD) function, Proximal Alternating Linearized Minimization(PALM), non-convex problem, clustering

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