A principal component analysis of interval data based on center and log-radius

被引：0
|
作者：
Zhao Q. [1 ,2 ]
Wang H. [1 ,3 ]
Wang S. [1 ,2 ]
机构：
[1] School of Economics and Management, Beihang University, Beijing
[2] Beijing Key Laboratory of Emergency Support Simulation Technologies for City Operations, Beijing
[3] Beijing Advanced Innovation Center for Big Data and Brain Computing, Beihang University, Beijing
来源：
Beijing Hangkong Hangtian Daxue Xuebao/Journal of Beijing University of Aeronautics and Astronautics | 2021年 / 47卷 / 07期
基金：
中国国家自然科学基金;
关键词：
Center and log-radius; Covariance matrix; Dimension reduction; Interval data; Principal Component Analysis (PCA);
D O I：
10.13700/j.bh.1001-5965.2020.0227
中图分类号：
学科分类号：
摘要：
In order to study the dimension reduction and visualization of multivariate interval data, a two-dimensional array including center and log-radius is used as the expression of interval data. Then the algebraic algorithm of interval data is given, and a new Principal Component Analysis (PCA) method of interval data is proposed on this basis. The processing of the logarithm of interval radius ensures the rationality that the range of the final interval principal components are non-negative. The calculation of this new method is simple, and the complexity is low. Furthermore, the change of the relative position between the points in the sample group before and after the dimension reduction is as small as possible. By reducing the dimension of variables in the high-dimensional space, various classical statistical analysis methods can be used. Besides, the sample points in the original high-dimensional space can be depicted in the low-dimensional space, which makes it possible to visualize multivariate interval data. The results of simulation experiment verify the effectiveness of the proposed method. © 2021, Editorial Board of JBUAA. All right reserved.
引用
收藏
页码：1414 / 1421
页数：7
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