A university map of course knowledge

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 can be informed by behavioral data and that domain knowledge can be extracted from this structure through visualization and a novel mapping of the text descriptions of elements onto this behaviorally informed representation. In this study, we use the course enrollment histories of 124,000 students at a public university to learn vector representations of its courses. From these course selection informed representations, a notable 88% of course attribute information was recovered, as well as 40% of course relationships constructed from prior domain knowledge and evaluated by analogy (e.g., Math 1B is to Honors Math 1B as Physics 7B is to Honors Physics 7B). 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 via regression. We find that representations learned from enrollment histories resolved courses to a level of semantic fidelity exceeding that of their catalog descriptions, revealing nuanced content differences between similar courses, as well as accurately describing departments the dataset had no course descriptions for. We end with a discussion of the possible mechanisms by which this semantic structure may be informed and implications for the nascent research and practice of data science.