函数型数据的1-范数主成分分析方法研究  

Research on 1-Norm Principal Component Analysis for Functional Data

作　　者：于凤敏 刘黎明[2] 于南翔 YU Feng-min;LIU Li-ming;YU Nan-xiang(Chongqing University of Posts and Telecommunications,Chongqing 400065,China;School of Statistics,Capital University of Economics and Business,Beijing 100071,China)

机构地区：[1]重庆邮电大学理学院,重庆400065 [2]首都经济贸易大学统计学院,北京100070

出　　处：《数理统计与管理》2021年第3期429-438,共10页Journal of Applied Statistics and Management

基　　金：北京市自然科学基金资助项目(9172003);国家自然科学基金资助项目(11601349).

摘　　要：本文以函数型数据为研究对象,首先介绍了传统的2-范数函数型主成分分析方法,并分析了2-范数下主成分权函数对异常值敏感的原因.针对原因,本文提出了1-范数函数型主成分分析方法,构建了1-范数主成分权函数的求解算法.最后利用加拿大温度数据和北京市空气质量数据对两种方法进行了对比分析,结果表明相较于2-范数的函数型主成分分析方法,1-范数的函数型主成分分析方法得到的主成分权函数更稳定,结果更可靠.This article takes functional data as the research object,Firstly,the traditional 2-norm functional principal component analysis method is introduced,and the reason why the principal component weight function is sensitive to outliers under 2-norm is analyzed.In view of the reasons,this paper presents a 1-norm functional principal component analysis method,and constructs an algorithm for solving the weight function of 1-norm functional principal component.Finally,the two methods were compared using Canadian temperature data and Beijing air quality data.The results show that compared with the 2-norm functional principal component analysis method,the principal component weight function obtained by the 1-norm functional principal component analysis method is more stable and the result is more reliable.

关 键 词：函数型数据 主成分 异常值 1-范数 稳健性 

分 类 号：O212[理学—概率论与数理统计]