A new gene subset selection approach based on linearly separating gene pairs

The concept of linear separability of gene expression data sets with respect to two classes, has been recently studied in literature. The problem is to efficiently find all pairs of genes which induce a linear separation of the data. It has been suggested that an underlying molecular mechanism relates together the two genes of a separating pair to the phenotype under study, such as a specific cancer. In this paper we study the Containment Angle (CA) defined on the unit circle for a linearly separable gene pair as a better alternative to the paired t-test ranking function for gene selection. Using the CA we also show empirically that a given classifier´s error is related to the degree of linear separability of a given data set. Finally we propose a new gene subset selection approach based on the CA ranking function. Our approach gives better results, in terms of subset size and classification accuracy when compared to well-performing methods, on many data sets.