Principal component and correspondence analysis of compositional data: some similarities

Abstract

Principal component and correspondence analysis can both be used as exploratory methods for representing multivariate data in two dimensions. Circumstances under which the, possibly inappropriate, application of principal components to untransformed compositional data approximates to a correspondence analysis of the raw data are noted. Aitchison (1986) has proposed a method for the principal component analysis of compositional data involving transformation of the raw data. It is shown how this can be approximated by a correspondence analysis of appropriately transformed data. The latter approach may be preferable when there are zeroes in the data.