Canonical Correlation Analysis based on Hilbert-Schmidt Independence Criterion and Centered Kernel Target Alignment

Abstract

Canonical correlation analysis (CCA) is a well established technique for identifying linear relationships among two variable sets. Kernel CCA (KCCA) is the most notable nonlinear extension but it lacks interpretability and robustness against irrelevant features. The aim of this article is to introduce two nonlinear CCA extensions that rely on the recently proposed Hilbert-Schmidt independence criterion and the centered kernel target alignment. These extensions determine linear projections that provide maximally dependent projected data pairs. The paper demonstrates that the use of linear projections allows removing irrelevant features, whilst extracting combinations of strongly associated features. This is exemplified through a simulation and the analysis of recorded data that are available in the literature. 1.