基于DDC算法的稳健稀疏主成分法及其实证研究  

A Robust Sparse Principle Component Analysis Based on DDC Algorithm and Its Empirical Study

作　　者：阮皓麟 王斌会[1] RUAN Hao-lin;WANG Bin-hui(Department of Business Management,School of Management,Jinan University,Guangzhou 510632,China)

机构地区：[1]暨南大学管理学院企管系,广东广州510632

出　　处：《数理统计与管理》2022年第4期662-678,共17页Journal of Applied Statistics and Management

基　　金：国家社科基金项目(16BTJ035)。

摘　　要：主成分分析是多元统计分析中经典降维方法之一,它有两个固有弊端:一是当样本中存在离群样本时,经典主成分法所得载荷向量、得分往往不符合实际;二是在现实中各主成分载荷往往都会不等于零,甚至经常还会出现次要变量与主要变量的载荷绝对值大小接近的情况,导致主成分可解释性被大幅削弱。另外,传统的稳健主成分法通过删除离群样本后计算载荷向量达到稳健效果,这对于那些只有少数几个变量的观测值离群的离群样本来说是一种欠妥的方法。针对上述几点,本文以DDC(Detecting Deviating Cell)算法为主要的稳健方法,提出一种稳健稀疏主成分法DDCSPCA。模拟实验和实证分析结果表明:DDCSPCA在处理有离群样本的数据时能达到稳健与(载荷向量)稀疏双重效果,而且,其对格离群数据有着以往稳健主成分法所远远不及的稳健性。Principal component analysis(PCA)isa classical dimensionality reduction method in multivariable analysis It has two disadvantages First,the classical PCA tends to obtain wrong loading vectors and score matrix when there are outliers in samples;second,the loadings of each PC are not equal tozero.In most cases,the(absolute values of)loadings of secondary variables are close tothose ofprimary variables,accounting for the weakened interpretability of PCs.Moreover,traditional robust PCAs achieve robustness by deleting outliers This is inappropriate for those outliers who have just afew outlying cells.In view of the above points,this paper proposed a robust sparse PCA DDCSPCA with DDC(Detecting Deviating Cell)algorithm as its main robust method In this paper,simulations and empirical studies on DDCSPCA are conducted,the results of which show that robustness and (loading vector)sparsity are achieved by applying DDCSPCA when there are outliers in data.Besides,DDCSPCA performs far better than traditional robust PCA in terms of robustness against cellwise outliers.

关 键 词：DDCSPCA 稳健稀疏主成分分析 格离群 

分 类 号：E910.3099[军事] O212[理学—概率论与数理统计]