Stability test of canonical correlation analysis for studying brain‐behavior relationships: The effects of subject‐to‐variable ratios and correlation strengths

Canonical correlation analysis (CCA), a multivariate approach to identifying correlations between two sets of variables, is becoming increasingly popular in neuroimaging studies on brain-behavior relationships. However, the CCA stability in neuroimaging applications has not been systematically investigated. Although it is known that the number of subjects should be greater than the number of variables due to the curse of dimensionality, it is unclear at what subject-to-variable ratios (SVR) and at what correlation strengths the CCA stability can be maintained. Here, we systematically assessed the CCA stability, in the context of investigating the relationship between the brain structural/functional imaging measures and the behavioral measures, by measuring the similarity of the first-mode canonical variables across randomly sampled subgroups of subjects from a large set of 936 healthy subjects. Specifically, we tested how the CCA stability changes with SVR under two different brain-behavior correlation strengths. The same tests were repeated using an independent data set (n = 700) for validation. The results confirmed that both SVR and correlation strength affect greatly the CCA stability-the CCA stability cannot be guaranteed if the SVR is not sufficiently high or the brain-behavior relationship is not sufficiently strong. Based on our quantitative characterization of CCA stability, we provided a practical guideline to help correct interpretation of CCA results and proper applications of CCA in neuroimaging studies on brain-behavior relationships.