高维稳健主成分聚类方法及其应用研究  

High-dimensional Robust Principal Component Clustering Method and Its Application

作　　者：姜云卢[1] 胡月 刘巧云 黄美兰 JIANG Yun-lu;HU Yue;LIU Qiao-yun;HUANG Mei-lan(School of Economics,Jinan University,Guangzhou 510632,China)

机构地区：[1]暨南大学经济学院,广东广州510632

出　　处：《数理统计与管理》2022年第1期1-10,共10页Journal of Applied Statistics and Management

基　　金：国家自然科学基金项目(12171203);广东省自然科学基金项目(2018A030313171,2019A1515011830)。

摘　　要：随着信息技术的高速发展,每条数据所包含的信息越来越丰富,使得数据不可避免地含有异常值,且随着维数的增加,异常值出现的可能性更大。传统的主成分聚类分析对异常值特別敏感,基于MCD估计的主成分聚类方法虽然对异常值具有防御作用,但是在高维数据下MCD估计的偏差过大,其稳健性显著降低,而且当维数大于观测值个数时MCD估计失效。为此本文提出了基于MRCD估计的稳健主成分聚类方法,数值模拟和实证分析表明,基于MRCD估计的主成分聚类分析的效果优于传统的主成分聚类分析和基于MCD估计的主成分聚类分析,尤其是在维数大于样本观测值的情况下,MRCD估计更为有效。With the rapid development of information technology,each piece of data contains more and more information,making the data inevitably contain outliers,and as the number of dimensions increases,outliers are more likely to appear.Traditional principal component clustering analysis is particularly sensitive to outliers.Although the principal component clustering method based on MCD estimation has defensive effects on outliers,the deviation of MCD estimation is too large under highdimensional data,and its robustness is significantly reduced.When the dimension is greater than the number of observations,the MCD estimation fails.Therefore,this paper proposes a robust principal component clustering method based on MRCD estimation.Numerical simulation and empirical analysis show that the effect of principal component clustering analysis based on MRCD estimation is better than traditional principal component clustering analysis and principal component based on MCD estimation.Cluster analysis,especially when the dimension is larger than the sample observations,MRCD estimation is more effective.

关 键 词：异常值 MCD估计 MRCD估计 主成分聚类分析 

分 类 号：O212[理学—概率论与数理统计]