Probabilistic functional integrated networks are powerful tools with which to draw inferences from high-throughput data. However, network analyses are generally not tailored to specific biological functions or processes. This problem may be overcome by extracting process-specific sub-networks, but this approach discards useful information and is of limited use in poorly annotated areas of the network. Here we describe an extension to existing integration methods which exploits dataset biases in order to emphasise interactions relevant to specific processes, without loss of data. We apply the method to high-throughput data for the yeast Saccharomyces cerevisiae, using Gene Ontology annotations for ageing and telomere maintenance as test processes. The resulting networks perform significantly better than unbiased networks for assigning function to unknown genes, and for clustering to identify important sets of interactions. We conclude that this integration method can be used to enhance network analysis with respect to specific processes of biological interest.