  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.
