稳健主成分分析方法的稳健性比较

doi:10.6040/j.issn.1671-9352.0.2024.120

《山东大学学报(理学版)》 ›› 2026, Vol. 61 ›› Issue (9): 49-55.doi: 10.6040/j.issn.1671-9352.0.2024.120

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稳健主成分分析方法的稳健性比较

方红燕,张巧巧,杨心雨

安徽大学大数据与统计学院, 安徽合肥 230601

发布日期:2026-09-30
作者简介:方红燕(1985— ),女,副教授,博士,研究方向为生物统计、统计计算、高维数据分析等. E-mail:fanhoy@ustc.edu.cn
基金资助:
安徽省新时代育人质量工程项目(2022jyjxggyj109);安徽大学大学生创新创业训练项目(S202310357252)

Robustness comparison of ROBPCA methods

FANG Hongyan, ZHANG Qiaoqiao, YANG Xinyu

School of Big Data and Statistics, Anhui University, Hefei 230601, Anhui, China

Published:2026-09-30

摘要/Abstract

摘要： 借助变点检测中的累积和控制图(cumulative sum chart, CUSUM)法,本文提出自适应的稳健主成分分析方法。通过大量的模拟试验,对比各稳健主成分分析方法在异常值筛选中的性能。基于CUSUM法的稳健主成分分析方法筛选后保留的样本大小最接近真实值,具有最高的筛选准确率,在变量维数变大时也有着更优异的表现。对浙江省各县市国民经济指标实际数据的分析应用也验证该方法筛选异常值的准确性和可靠性。

关键词: 稳健主成分分析, 异常值, PCA方法, MCD方法, FAST-MCD方法, ROBPCA方法, 变点检测, CUSUM法

Abstract: An adaptive robust PCA method is developed by employing the CUSUM chart method in change point detection. The outlier detection performances of robust PCA methods are compared through numerous simulation studies. The robust PCA based on the CUSUM chart method obtains the closest sample size to the true value, has the highest screening accuracy, and has a superior performance even when the variable dimension becomes larger. The analysis and application of the actual data of national economic indicators in counties and cities in Zhejiang province also verifies the accuracy and reliability of this method.

Key words: ROBPCA, outliers, PCA method, MCD method, FAST-MCD method, ROBPCA method, change point detection, CUSUM method

中图分类号:

O212

方红燕,张巧巧,杨心雨. 稳健主成分分析方法的稳健性比较[J]. 《山东大学学报(理学版)》, 2026, 61(9): 49-55.

FANG Hongyan, ZHANG Qiaoqiao, YANG Xinyu. Robustness comparison of ROBPCA methods[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2026, 61(9): 49-55.

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稳健主成分分析方法的稳健性比较

Robustness comparison of ROBPCA methods

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