Principal component analysis of compositional data

SUMMARY 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.