To detect key TF-TG subnetworks (modules) from the cell population TF–TG trans-regulation, we used non-negative matrix factorization (NMF). Before matrix factorization, We normalized the trans-regulatory potential matrix by standardizing each row (TF) and each column (TG) independently. The standardization of each TF ensures that for each TF, the average regulatory potential across TGs becomes zero, and the variation in regulatory potential across genes has a standard deviation of one. The same normalization was applied to each TG, so that the effect of the regulator side was also normalized. We took the average of these two standardized matrices and set the negative values to zeros, which was used for downstream analysis. Next, we performed NMF on the preprocessed matrix to decompose it into two non-negative matrices, W and H, representing module membership of TGs and TFs, respectively. W is a m by k module weight matrix for TF, representing module weight of TF, where m is the number of TF. H is a k by n matrix, representing module weight for TGs, where n is the number of TG. To assign
