Some remarks on the functional relation between canonical correlation analysis and partial least squares

Abstract

This paper deals with the functional relation between multivariate methods of canonical correlation analysis (CCA), partial least squares (PLS) and also their kernelized versions. Both methods are determined by the solution of the respective optimization problem, and result in algorithms using spectral or singular decomposition theories. The solution of the parameterized optimization problem, where the boundary points of a parameter give exactly the results of CCA (resp. PLS) method leads to the vector functions (paths) of eigenvalues and eigenvectors or singular values and singular vectors. Specifically, in this paper, the functional relation means the description of classes into which the given paths belong. It is shown that if input data are analytical (resp. smooth) functions of a parameter, then the vector functions are also analytical (resp. smooth). Those approaches are studied on three practical examples of European tourism data.