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The Pearson correlation is the simplest and computationally most efficient similarity measure for gene expression profiles. For genes $i$ and $j$, their Pearson correlation can be written as $$\label{eq:1}
  C_{ij}=\sum_{l=1}^nX_{il}X_{jl}\,.$$ In matrix notation, this can be combined as the matrix multiplication [$${\mathbf{C}}={\mathbf{X}}{\mathbf{X}}^T.$$]{}

Gene pairs with large positive or negative correlation values tend to be up- or down-regulated together, due to either a direct regulatory link between them, or being jointly co-regulated by a third, often hidden, factor. By filtering for correlation values exceeding a significance threshold determined by comparison with randomly permuted data, a discrete co-expression network is obtained. Assuming that a high degree of co-expression signifies that genes are involved in the same biological processes, graph theoretical methods can be employed, for instance, to predict gene function [@sharan2007network].

One drawback of the Pearson correlation is that by definition it is biased towards *linear* associations. To overcome this limitation, other measures are available. The Spearman correlation uses expression data ranks (cf. Section \[sec:genet-gene-expr\]) in Equation , and will give high score to *monotonic* relations. Mutual information is the most general measure and detects both linear and non-linear associations. For a pair of discrete random variables $A$ and $B$ (representing 