基于邻近交替线性化的稀疏非负矩阵分解算法  

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

作　　者：王静 杨丹[1,2] WANG Jing;YANG Dan(College of Mathematics and Statistics,Chongqing University,Chongqing 401331,China;School of Software Engineering,Chongqing University,Chongqing 401331,China)

机构地区：[1]重庆大学数学与统计学院,重庆401331 [2]重庆大学软件学院,重庆401331

出　　处：《计算机工程》2019年第2期220-225,232,共7页Computer Engineering

基　　金：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)

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。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 L 0 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.

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 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]