Principal Component Analysis of Compositional Data
针对成分数据分量之和为1的约束及数据曲率问题，通过改进变换技术提出对数线性对比形式的主成分分析，并展示其应用优势。
Compositional data, consisting of vectors of proportions, have proved difficult to handle statistically because of the awkward constraint that the components of each vector must sum to unity. Moreover such data sets frequently display marked curvature so that linear techniques such as standard principal component analysis are likely to prove inadequate. From a critical reexamination of previous approaches we evolve, through adaptation of recently introduced transformation techniques for compositional data analysis, a log linear contrast form of principal component analysis and illustrate its advantages in applications.