Gene Expression Array Exploration Using K-Formal Concept Analysis

DNA micro-arrays are a mechanism for eliciting gene expression values, the concentration of the transcription products of a set of genes, under different chemical conditions. The phenomena of interest-up-regulation, down-regulation and co-regulation-are hypothesized to stem from the functional relationships among transcription products. In [1,2,3] a generalisation of Formal Concept Analysis was developed with data mining applications in mind, K-Formal Concept Analysis, where incidences take values in certain kinds of semirings, instead of the usual Boolean carrier set. In this paper, we use ((R) over bar (min),(+))- and ((R) over bar (max),(+))-Formal Concept Analysis to analyse gene expression data for Arabidopsis thaliana. We introduce the mechanism to render the data in the appropriate algebra and profit by the wealth of different Galois Connections available in Generalized Formal Concept Analysis to carry different analysis for up- and down-regulated genes.