基于中心-对数半长的区间数据主成分分析

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.