  Knowledge representation has gained in relevance as data from the ubiquitous
digitization of behaviors amass and academia and industry seek methods to
understand and reason about the information they encode. Success in this
pursuit has emerged with data from natural language, where skip-grams and other
linear connectionist models of distributed representation have surfaced
scrutable relational structures which have also served as artifacts of
anthropological interest. Natural language is, however, only a fraction of the
big data deluge. Here we show that latent semantic structure, comprised of
elements from digital records of our interactions, can be informed by
behavioral data and that domain knowledge can be extracted from this structure
through visualization and a novel mapping of the literal descriptions of
elements onto this behaviorally informed representation. We use the course
enrollment behaviors of 124,000 students at a public university to learn vector
representations of its courses. From these behaviorally informed
representations, a notable 88% of course attribute information were recovered
(e.g., department and division), as well as 40% of course relationships
constructed from prior domain knowledge and evaluated by analogy (e.g., Math 1B
is to Math H1B as Physics 7B is to Physics H7B). To aid in interpretation of
the learned structure, we create a semantic interpolation, translating course
vectors to a bag-of-words of their respective catalog descriptions. We find
that the representations learned from enrollments resolved course vectors to a
level of semantic fidelity exceeding that of their catalog descriptions,
depicting a vector space of high conceptual rationality. We end with a
discussion of the possible mechanisms by which this knowledge structure may be
informed and its implications for data science.
