Mihalik, Agoston;
Chapman, James;
Adams, Rick A;
Winter, Nils R;
Ferreira, Fabio S;
Shawe-Taylor, John;
Mourão-Miranda, Janaina;
(2022)
Canonical Correlation Analysis and Partial Least Squares for identifying brain-behaviour associations: a tutorial and a comparative study.
Biological Psychiatry: Cognitive Neuroscience and Neuroimaging
, 7
(11)
pp. 1055-1067.
10.1016/j.bpsc.2022.07.012.
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Abstract
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 explain their main advantages and disadvantages. We highlight crucial aspects of the CCA/PLS analysis framework, including optimising the hyperparameters of the model and testing the identified associations for statistical significance. We apply the described CCA/PLS models to simulated data and real data from the Human Connectome Project and the Alzheimer's Disease Neuroimaging Initiative (both of n>500). We use both low and high dimensionality versions of each data (i.e., ratios between sample size and variables in the range of ∼1-10 and ∼0.1-0.01) to demonstrate the impact of data dimensionality on the models. Finally, we summarize the key lessons of the tutorial.
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