Compositional Canonical Correlation Analysis

Abstract

The study of the relationships between two compositions by means of canonical correlation analysis is addressed A coimnositional version of canonical correlation analysis is developed. and called CODA-CCO. We consider two approaches, using the centred log-ratio transformation and the calculation of all possible pairwise log-ratios within sets. The relationships between both approaches are pointed out, and their merits are discussed. The related covariance matrices are structurally singular, and this is efficiently dealt with by using generalized inverses. We develop compositional canonical biplots and detail their properties. The canonical biplots are shown to be powerful tools for discovering the most salient relationships between two compositions. Some guidelines for compositional canonical biplots construction are discussed. A geological data set with X-ray fluorescence spectrometry measurements on major oxides and trace elements is used to illustrate the proposed method. The relationships between an analysis based on centred log-ratios and on isometric log-ratios are also shown.