• 论文 •

基于中心-对数半长的区间数据主成分分析

1. 1. 北京航空航天大学 经济管理学院, 北京 100083;
2. 城市运行应急保障模拟技术北京市重点实验室, 北京 100083;
3. 北京航空航天大学 大数据科学与脑机智能高精尖创新中心, 北京 100083
• 收稿日期:2020-05-29 发布日期:2021-08-06
• 通讯作者: 王珊珊 E-mail:sswang@buaa.edu.cn
• 基金资助:
国家自然科学基金（71420107025，11701023）

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

ZHAO Qing1,2, WANG Huiwen1,3, WANG Shanshan1,2

1. 1. School of Economics and Management, Beihang University, Beijing 100083, China;
2. Beijing Key Laboratory of Emergency Support Simulation Technologies for City Operations, Beijing 100083, China;
3. Beijing Advanced Innovation Center for Big Data and Brain Computing, Beihang University, Beijing 100083, China
• Received:2020-05-29 Published:2021-08-06
• Supported by:
National Natural Science Foundation of China (71420107025,11701023)

Abstract: 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.