Module summarization by Eigengene network

After constructing the consensus modules using hierarchical clustering technique as described above, we have summarized each consensus module expression profile by one representative gene: the module eigengene. Module eigengene is defined as the first right singular vector of a module expression matrix. Let, C(k)=(cij(k)) refers to the gene expression data corresponding to module k, where index i=1,2,…,p corresponds to the module genes and the index j=1,2,…,q corresponds to the microarray samples, and each row of C ^(k), has been standardized to mean 0 and variance 1. The singular value decomposition of C ^(k)[p x q] is defined as:

where, the columns of the orthogonal matrices U=(u ₁,u ₂,…,u _(min(p,q))) and V=(v ₁,v ₂,…,v _(min(p,q))) are the left- and right-singular vectors, respectively, and D=(d ₁,d ₂,…,d _(min(p,q))) is a diagonal matrix containing singular values. Incorporating terminology from [17, 40–42], the first column of V ^(k) is referred to as the Module Eigengene:

Let, M E _I and M E _J denote the module eigengenes of the I ^th and J ^th modules, respectively, then the connection strength between eigengenes M E _I and M E _J is expressed as:

Eigengenes of different modules of a gene co-expression network often exhibit correlations which we have used to constitute eigengene network [21]: A d j _Eigen, which is defined as follows:

Eigengenes of different consensus modules often exhibit correlations which we have used to constitute consensus eigengene networks: