Principal component analysis for compositional data vectors

Since Aitchison’s founding research work, compositional data analysis has attracted growing attention in recent decades. As a powerful technique for exploratory analysis, principal component analysis (PCA) has been extended to compositional data. Despite extensive efforts in PCA on compositional data parts as variables, this paper contributes to modeling PCA for compositional data vectors. Based on algebraic operators in Simplex space, the PCA process is deduced and transformed into calculating some inner products. Properties of principal components are also investigated. Two real-data examples illustrate the merits of the proposed PCA for compositional data vectors.