Figure 2

Matrix T _coexp : decomposition of the matrix T . Decomposing biological functions into coexpressed biological functions leads to build the matrix T _{c o e x p} where a row represents a gene and a column a coexpressed biological function. The general term of T _{c o e x p} , $T_{\mathit{\text{kj}}}{\mathbb{1}}_{k\in K_l^j}$ equals 1 if the gene k is associated with the function j and if it belongs to the cluster $K_l^j$, 0 else wise. The column margin of the coexpressed biological function l is equal to the number of genes in the corresponding cluster, that is $\mathit{\text{card}}\left(K_l^j\right)$. In addition, for every function j, the sum of the column margins associated with the coexpressed biological functions derived from j is equal to the column margin associated with the function j: ${\sum }_{l=1}^{L_j}\mathit{\text{card}}\left(K_l^j\right)=T_{\mathrm{.j}}$. Finally, we can remark that the row margins and the total number of associations are equal to those from T.