Motivation: The rapid growth of diverse biological data allows us to consider interactions between a variety of objects, such as genes, chemicals, molecular signatures, diseases, pathways and environmental exposures. Often, any pair of objects--such as a gene and a disease--can be related in different ways, for example, directly via gene-disease associations or indirectly via functional annotations, chemicals and pathways... Different ways of relating these objects carry different semantic meanings. However, traditional methods disregard these semantics and thus cannot fully exploit their value in data modeling. Results: We present Medusa, an approach to detect size-k modules of objects that, taken together, appear most significant to another set of objects. Medusa operates on large-scale collections of heterogeneous data sets and explicitly distinguishes between diverse data semantics. It advances research along two dimensions: it builds on collective matrix factorization to derive different semantics, and it formulates the growing of the modules as a submodular optimization program. Medusa is flexible in choosing or combining semantic meanings and provides theoretical guarantees about detection quality. In a systematic study on 310 complex diseases, we show the effectiveness of Medusa in associating genes with diseases and detecting disease modules. We demonstrate that in predicting gene-disease associations Medusa compares favorably to methods that ignore diverse semantic meanings. We find that the utility of different semantics depends on disease categories and that, overall, Medusa recovers disease modules more accurately when combining different semantics. (read more)