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High-throughput genomic measurements, interpreted as cooccurring data samples from multiple sources, open up a fresh problem for machine learning: What is in common in the different data sets, that is, what kind of statistical dependencies are there between the paired samples from the different sets? We introduce a clustering algorithm for exploring the dependencies. Samples within each data set are grouped such that the dependencies between groups of different sets capture as much of pairwise dependencies between the samples as possible. We formalize this problem in a novel probabilistic way, as optimization of a Bayes factor. The method is applied to reveal commonalities and exceptions in gene expression between organisms and to suggest regulatory interactions in the form of dependencies between gene expression profiles and regulator binding patterns.