Canonical correlation analysis and partial least squares for identifying brain-behaviour associations: a tutorial and a comparative study

Canonical Correlation Analysis (CCA) and Partial Least Squares (PLS) are powerful multivariate methods for capturing associations across two modalities of data (e.g., brain and behaviour). However, when the sample size is similar or smaller than the number of variables in the data, CCA and PLS models may overfit, i.e., find spurious associations that generalise poorly to new data. Dimensionality reduction and regularized extensions of CCA and PLS have been proposed to address this problem, yet most studies using these approaches have some limitations. This work gives a theoretical and practical introduction into the most common CCA/PLS models and their regularized variants. We examine the limitations of standard CCA and PLS when the sample size is similar or smaller than the number of variables. We discuss how dimensionality reduction and regularization techniques address this problem and …