It is commonly accepted that genes with similar expression profiles
are functionally related. However, so far no clear distinction has been made as for the type of the functional link between genes as suggested by microarray data. Similarly expressed genes can be part of the same complex as interacting partners; they can participate in the same pathway without interacting directly; they can perform similar functions; or they can simply have similar regulatory sequences. Here we embark on a rigorous study of the notion of functional link as implied from expression data. We analyze different similarity measures of gene expression profiles and assess their usefulness and robustness in detecting biological relationships by comparing the similarity scores with results obtained from databases of interacting proteins, promoter signals, and cellular pathways, as well as through sequence comparisons and pathway modeling. We also introduce new similarity measures we specifically developed for the analysis of expression data. These measures are based on statistical analysis and better discriminate genes which are functionally nearby and faraway. With the optimized similarity measures we proceed to analyze other aspects of this data. Specifically, we introduce a method of inferring the type of relationship by correlating the expression data with all the other data sets. This method allows us to not only predict when genes are functionally related but also to suggest how they are related. We then cluster the data using clustering algorithms that are specially tailored to deal with noisy data. Finally we propose methods for assessing the significance of clusters and study the correspondence between gene clusters and biochemical pathways.