基于一种非凸罚函数的稀疏主成分分析方法  

Sparse Principal Component Analysis Based on a Nonconvex Penalty Function

作　　者：余嘉月 张倩 李海洋[1] YU Jiayue;ZHANG Qian;LI Haiyang(School of Science,Xi’an Polytechnic University,Xi’an 710048,China;School of Computer Science and Engineering,University of Electronic Science and Technology,Chengdu 611731,China)

机构地区：[1]西安工程大学理学院,西安710048 [2]电子科技大学计算机科学与工程学院,成都611731

出　　处：《河南科学》2019年第9期1385-1389,共5页Henan Science

基　　金：国家自然科学基金项目(11271297)

摘　　要：稀疏主成分分析方法剔除了与主成分关系不密切的原始变量,保留了与主成分关系密切的原始变量,克服了经典主成分分析方法的不足.在稀疏主成分分析的基础上,用一种收缩算子所对应的非凸罚函数替代稀疏主成分分析中的L1罚,提出了基于非凸罚函数的稀疏主成分分析方法,并给出了阈值迭代算法.结果表明,该方法相对于稀疏主成分分析方法,不仅提高了总方差贡献率,而且增加了主成分载荷的稀疏度,即更加凸显主成分与某些原始变量的关系.Sparse principal component analysis eliminates the original variables that are not closely related to principal components,retains the original variables that are closely related to principal components,and overcomes the shortcomings of classical principal component analysis. Based on sparse principal component analysis,we use a nonconvex penalty function which is corresponding to a contraction operator to replace the L1 penalty in sparse principal component analysis,and propose a new method,which is called sparse principal component analysis based on a nonconvex penalty function. The experimental results show that,compared with the sparse principal component analysis method,the new algorithm not only improves the percentage of variance,but also increases the sparsity of principal component loadings.

关 键 词：稀疏主成分分析 阈值迭代算法 非凸罚函数 稀疏信息处理 收缩算子 临近算子 

分 类 号：O213[理学—概率论与数理统计]