基于主成分分析的成分数据缺失值插补法  

Imputation of Missing Values for Compositional Data Based on Principal Component Analysis

作　　者：张晓琴[1] 王敏[1] 

机构地区：[1]山西大学数学科学学院,太原030006

出　　处：《应用概率统计》2016年第1期101-110,共10页Chinese Journal of Applied Probability and Statistics

基　　金：山西省自然科学基金面上项目(2015011044);山西省国际科技合作计划项目(2015081020)资助

摘　　要：本文针对成分数据的特殊几何结构,提出了两种新方法对成分数据缺失值进行插补.一种是用单形空间的均值进行插补,主要是用Aitchison足巨离找到含缺失值样本的k个近邻样本,再结合单形空间中的加法运算与数乘运算,用单形空间上的均值对成分数据的缺失值进行插补;另一种是用主成分回归方法进行插补,先将用第一种方法进行初始插补的成分数据经过等距对数比变换变成普通数据,再用主成分回归进行第二次插补.实例分析和实验模拟结果表明:与k近邻插补法、迭代的最小二乘插补法相比较,本文提出的主成分插补法更优.In this paper, considering of the special geometry of compositional data, two new methods for estimating missing values in compositional data are introduced. The first method uses the mean in the simplex space which mainly finds the k-nearest neighbor procedure based on the Aitchison distance, combining with two basic operations on the simplex, perturbation and powering. As a second proposal the principal component regression imputation method is introduced which initially starts from the result of the proposed the mean in the simplex. The method uses ilr transformation to transform the compositional data set, and then uses principal component regression in a transformed space. The proposed methods are tested on real data and simulated data sets, the results show that the proposed methods work well.

关 键 词：成分数据 缺失值插补 Aitchison距离 单形空间 主成分回归 

分 类 号：O212.1[理学—概率论与数理统计]