Addressing the mean-correlation relationship in co-expression analysis

Estimates of correlation between pairs of genes in co-expression analysis are commonly used to construct networks among genes using gene expression data. As previously noted, the distribution of such correlations depends on the observed expression level of the involved genes, which we refer to this as a mean-correlation relationship in RNA-seq data, both bulk and single-cell. This dependence introduces an unwanted technical bias in co-expression analysis whereby highly expressed genes are more likely to be highly correlated. Such a relationship is not observed in protein-protein interaction data, suggesting that it is not reflecting biology. Ignoring this bias can lead to missing potentially biologically relevant pairs of genes that are lowly expressed, such as transcription factors. To address this problem, we introduce spatial quantile normalization (SpQN), a method for normalizing local distributions in a correlation matrix. We show that spatial quantile normalization removes the mean-correlation relationship and corrects the expression bias in network reconstruction.