Canonical Correlation Analysis and Partial Least Squares for Identifying Brain-Behavior Associations: A Tutorial and...

Area of Science:

• Multivariate statistics
• Neuroimaging analysis
• Statistical modeling

Background:

• Canonical correlation analysis (CCA) and partial least squares (PLS) are key for analyzing associations between two data modalities, such as brain imaging and behavioral data.
• Standard CCA and PLS models are prone to overfitting when the number of variables approaches or exceeds the sample size, leading to unreliable findings.

Purpose of the Study:

• To provide a theoretical and practical introduction to common CCA/PLS models and their regularized extensions.
• To examine the limitations of standard CCA/PLS in high-dimensional data scenarios (sample size similar to or smaller than the number of variables).
• To discuss how dimensionality reduction and regularization address overfitting and improve model generalization.

Main Methods:

• Review of standard and regularized CCA/PLS models.
• Discussion of dimensionality reduction techniques.
• Hyperparameter optimization and statistical significance testing for CCA/PLS.
• Application to simulated data and real-world datasets (Human Connectome Project, ADNI) with varying dimensionality.

Main Results:

• Demonstration of overfitting in standard CCA/PLS with high-dimensional data.
• Illustration of how regularization and dimensionality reduction mitigate overfitting and enhance generalizability.
• Impact of data dimensionality on CCA/PLS model performance is shown.

Conclusions:

• Regularized CCA/PLS variants and dimensionality reduction are essential for reliable analysis of high-dimensional data.
• Proper model selection, hyperparameter tuning, and significance testing are critical for valid CCA/PLS applications.
• This tutorial provides practical insights for researchers using CCA/PLS in fields like neuroimaging.