Spectral analysis of gene expression profiles using gene networks

Microarrays have become extremely useful for analysing genetic phenomena, but establishing a relation between microarray analysis results (typically a list of genes) and their biological significance is often difficult. Currently, the standard approach is to map a posteriori the results onto gene networks to elucidate the functions perturbed at the level of pathways. However, integrating a priori knowledge of the gene networks could help in the statistical analysis of gene expression data and in their biological interpretation. Here we propose a method to integrate a priori the knowledge of a gene network in the analysis of gene expression data. The approach is based on the spectral decomposition of gene expression profiles with respect to the eigenfunctions of the graph, resulting in an attenuation of the high-frequency components of the expression profiles with respect to the topology of the graph. We show how to derive unsupervised and supervised classification algorithms of expression profiles, resulting in classifiers with biological relevance. We applied the method to the analysis of a set of expression profiles from irradiated and non-irradiated yeast strains. It performed at least as well as the usual classification but provides much more biologically relevant results and allows a direct biological interpretation

Partition Decoupling for Multi-gene Analysis of Gene Expression Profiling Data

We present the extention and application of a new unsupervised statistical learning technique--the Partition Decoupling Method--to gene expression data. Because it has the ability to reveal non-linear and non-convex geometries present in the data, the PDM is an improvement over typical gene expression analysis algorithms, permitting a multi-gene analysis that can reveal phenotypic differences even when the individual genes do not exhibit differential expression. Here, we apply the PDM to publicly-available gene expression data sets, and demonstrate that we are able to identify cell types and treatments with higher accuracy than is obtained through other approaches. By applying it in a pathway-by-pathway fashion, we demonstrate how the PDM may be used to find sets of mechanistically-related genes that discriminate phenotypes.Comment: Revise