Partial Least Squares for Compositional Canonical Correlation

Compositional data are quantitative descriptions of the parts of some whole, conveying relative information. The relationship between two sets of compositional descriptors can be explored by use of Canonical Correlation analysis with a procedure based on Partial Least Squares (PLS). This method offers a way to deal with matrix singularity in an efficient fashion and presents the further advantage of being easy to interpret. In order to fully explore the potential of PLS for analyzing the relationships between two sets of compositions, the performances of the NIPALS, SIMPLS and Kernel algorithms are compared on simulated data.