Figure 3

Gene expression matrix, (A), formal concepts (B) and QSQ (C). In A is shown a toy example of a gene expression matrix displaying the level of expression of 4 genes (G1 – G4) in 4 biological situations (S1 – S4). In order to extract formal concepts, one has first to encode some gene expression property. We decided to encode the over-expression by applying the mid-range method [11]. One first defines a threshold per gene (max value – min value)/2 – min value). For the G1 gene, this threshold = 62.5. All expression values below or equal to the threshold are considered null, all values strictly above the threshold are set to 1. This allows to create the binary matrix (B). One then extracts all formal concepts from such a matrix. It consists of a bi-set of genes and situations such that all genes are simultaneously over-expressed in the situations, and such that neither gene nor situation can be added without introducing a null value (those are maximal bi-sets). From the toy example, three formal concepts can be extracted (shown below the B matrix). It is immediately apparent that the two first concepts are closely related. It is therefore tempting to aggregate them, allowing the creation of a Quasi-synexpression group (QSG; [17]) containing three genes and three situations. One possible representation of a QSG is shown in C, the values indicating the number of formal concepts supporting the Gene-to-Situation association.