Fast Identification of Similarly Expressed Genes

One of the most important problems in modern genomics is to identify which genes are responsible for an specific phenomenon within the cell. This problem can be partially answered by comparing expression data from two sets of related experiments, for instance a set of cancerous and a set of healthy cells, and genes with similar expression level. Unfortunately, the number of genes is usually much larger than the number of available expression data, and to find the best candidates is in general difficult and time consuming. We propose a different and simple representation of the expression data which allows a very quick way to establish of how potentially related a gene is to each subset: instead of representing p microarrays, each containing N genes spotted, as a set of p labelled points in IR , we simply transpose the matrix and and represent the p experiments as N points in IR. In this new representation, the axis are labelled according to the experiment they represent and the IR can be decomposed in a cartesian product of subspaces S0,S1, . . .Sm. A point in this space represents a single gene and its projection on the subspace Si indicates the behavior of that gene in the i class. Consider a gene g and its projection gi on Si. By analyzing the projection and the distance of gi to the diagonal of Si, it is possible to generate several simple and significant metrics to evaluate the influence (or its absence) of g. The Fischer linear separator, for instance, has a straightforward geometric interpretation in this setup. The computation of most metrics takes linear time in N . A simple sort can then be used to identify the 1The line generated by the vector (1, 1, . . . , 1) most and least significant ones, with an execution time extremely short (less than a second with 4000 genes and 50 samples on a Pentium III). The method does not take into account groups of genes, but can be very useful for discarding uninteresting or pinpoint the most significant genes before applying more sophisticated techniques. Some interaction among genes can be modeled in the metric definition and in the sort criteria. For p ≤ 3, representing the genes only by their projections in the diagonals of S∗ is a very interesting way to visualize the whole dataset. Experimental results using known data indicate that the selection made by this method has a large intersection with that made by much more expensive algorithms.