两种区间数据主成分分析方法的比较研究

A Comparison Study of Two Methods for Principal Component Analysis of Interval Data

摘要: 针对顶点主成分分析算法(VPCA)计算量会随着变量个数的增加而按指数速度增长的问题,Cazes P提出一种简化算法,通过直接计算VPCA的相关系数矩阵,可以消除大量的冗余计算,解决VPCA的维数灾难问题。文章通过对这两种方法的计算过程和计算结果进行比较,说明这两种方法在计算结果上是完全等价的,但是,Cazes P提出的简化算法的计算过程更简单、所占据的存储空间更小、计算速度更快,实验分析进一步验证了理论分析的相关结论。

Abstract: A simplified method of VPCA was raised by Cazes P. The proposed method eliminates large amounts of redundant computation by calculating correlation matrix of the vertices matrix directly. A comparison study of VPCA and the simplified method shows that the two methods lead to the same results. However, the simplified method has higher speed and smaller occupied-space. An empirical analysis verified the conclusion of theoretical analysis.