Box 5 | Co-expression Measurements Gene co-expression is widely used for functional annotation, pathway analysis, and the reconstruction of gene regulatory networks. Co-expression measurements assess the similarity between a pair of gene expression profiles by detecting bivariate associations between them. These co-expression measurements can be summarized in five categories (Kumari et al. 2012; Allen et al. 2012; Song et al. 2012; Wang et al. 2014):

Correlation The most widely used co-expression measure is Pearson correlation, due to its straightforward conceptual interpretation and computational efficiency. However, Pearson correlation can only capture linear relationships between variables. Alternatively, Spearman correlation is a nonparametric measure of non-linear associations. Other correlation-based methods include Renyi correlation, Kendall rank correlation, and bi-weight mid-correlation.

Partial correlation Partial correlation is used to measure direct relationships between a pair of variables, excluding indirect relationships. Based on Gaussian graphical models, partial correlations infer conditional dependency as the non-zero entries in the precision matrix (the inverse of the covariance matrix).

Mutual-Information Mutual information-based methods measure general statistical dependence between two variables. Based on information theory, mutual information does not assume monotonic relationships and hence can capture non-linear dependencies.

Other measures Euclidian distance; Cosine similarity; Kullback-Leibler divergence; Hoeffding’s D, distance covariance, and probabilistic measures (as used in Baysian networks).