This paper on cell-cycle yeast genes suggests a method of hierarchical clustering by phased expression patterns. Once the clusters were calculated, the authors investigated and classified groups of cycle-related genes by function, such as metabolism or DNA replication, etc. Perhaps it might inspire further research on your part, based on your data.

I'm not entirely clear on what you are asking to do. If you're trying to identify clusters of "genes having same functions/protein products" I would think you would have to show homology to known (or even uncharacterized, but homologous) motifs. I would do this using similarity searchers (BLAST, BLAT, etc.) and ultimately with phylogenetic methods. Both homologous search methods such as BLAST (that infers homology) and phylogenetic methods are covered with daily questions here in this forum.

One reason that windowing might not give a complete answer is long-range regulatory interactions that would fall outside this window. The Dekker lab has investigated 5C-based approaches to this study. Their work may also be generally insightful.