Identification of linked GMV-SNP pairs in discovery dataset using spICA

We performed spICA to decompose 341 adults’ reconstructed GMV and SNP data into three independent GMV components and 37 independent SNP components (Fig. ​(Fig.1a).1a). Multivariate spICA decomposes GMV (X_g) and SNP (X_s) data into the product of a loading matrix (A_g, A_S for GMV and SNP, respectively) and a component matrix (S_g,S_s for GMV and SNP, respectively, X_g = A_g×S_g, X_s = A_s × S_s). Each row of the component matrix (S_g or S_s) is one independent brain/genomic component and each brain/genomic component is statistically independent of other brain/genomic components, thus enabling component/network-based analyses. Values in one brain/genomic component reflect the contributions of individual variables (voxels/SNPs) to the brain/genomic component. Each column of the loading matrix (A_g or A_s) is the loading vector, and values of the loading vector represent weights of the corresponding brain/genomic component across participants. The sparsity control in spICA regulates the number of major contributing variables for each brain and genomic component. The spICA code will be released in the Fusion ICA Toolbox (FIT, https://trendscenter.org/software/fit).

The GMV component number was set to three due to an expectation that the decomposed GMV components would resemble the three predefined ROIs (ICs 2–4 in Fig. S1). The sparsity regularizer was initialized as one. No sparsity constraint was imposed on GMV data since signals can be easily separated from backgrounds for these three ROI priors. The Hoyer constraint threshold of SNP data was set as 0.4 based on the estimation strategy described in our previous paper [54]. The SNP component number was estimated based on Chen’s consistency measure [62]. Ten runs of spICA were performed, and ICASSO [63] was employed to select the most stable run to calculate GMV-SNP associations. Bonferroni correction was applied at p < 0.05 for comparison of 3*37 GMV-SNP associations.