  We develop a systematic approach to measuring combinatorial innovation in the
biomedical sciences based upon the comprehensive ontology of Medical Subject
Headings (MeSH). This approach leverages an expert-defined knowledge ontology
that features both breadth (27,875 MeSH analyzed across 25 million articles
indexed by PubMed from 1902 onwards) and depth (we differentiate between Major
and Minor MeSH terms to identify differences in the knowledge network
representation constructed from primary research topics only). With this level
of uniform resolution we differentiate between three different modes of
innovation contributing to the combinatorial knowledge network: (i) conceptual
innovation associated with the emergence of new concepts and entities (measured
as the entry of new MeSH); and (ii) recombinant innovation, associated with the
emergence of new combinations, which itself consists of two types: peripheral
(i.e., combinations involving new knowledge) and core (combinations comprised
of pre-existing knowledge only). Another relevant question we seek to address
is whether examining triplet and quartet combinations, in addition to the more
traditional dyadic or pairwise combinations, provide evidence of any new
phenomena associated with higher-order combinations. Analysis of the size,
growth, and coverage of combinatorial innovation yield results that are largely
independent of the combination order, thereby suggesting that the common dyadic
approach is sufficient to capture essential phenomena. Our main results are
twofold: (a) despite the persistent addition of new MeSH terms, the network is
densifying over time meaning that scholars are increasingly exploring and
realizing the vast space of all knowledge combinations; and (b) conceptual
innovation is increasingly concentrated within single research articles, a
harbinger of the recent paradigm shift towards convergence science.
