Parallel ICA, as an extension of ICA, computes the same factorization of X, except it does it on two sets of observations, X1 and X2, simultaneously with an added constraint on the correlation between loading coefficients A1 and A2. By using this algorithm, components of different brain regions can be linked with components of different alcohol use assessments through correlated loading patterns across subjects. And thus parallel ICA is able to extract the brain volume variation associated with AUD severity, if the correlation between loading patterns is significant. After parallel ICA, the identified significantly correlated brain volume and alcohol use disorder components are used to test the potential CNVs’ effect on AUD. The procedure is summarized in the following steps:
