基于时变距离函数的多变量区间函数型主成分分析方法

A multivariable interval functional principal component analysis based on time-varying distance function

针对现实中经符号分析形成的区间函数型数据,提出时变距离函数概念,并将其应用于区间协方差计算.利用函数型主成分分析方法推导出相应的特征函数,提出了基于时变距离函数的多变量区间函数型主成分分析方法.通过实证证明:区间函数型主成分分析以区间化获取了更多信息,以函数化放松了假定,增加了可视化水平,能够有效解决区间函数型数据的特征提取和综合评价问题.

In this paper,a new concept of time-varying function is proposed to analyze interval functional data formed by symbolic data analysis and applied to the calculation of interval covariance.The corresponding characteristic function is derived by using functional principal component analysis,then interval functional principal component analysis for multivariable is put forward.The empirical analysis shows that the new interval functional principal component analysis can obtain more infor-mation by interval form,relax the hypothesis and increase the visualization level by function form,and it can effectively solve the problem of feature extraction and comprehensive evaluation of interval functional data.