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Topic discovery has witnessed a significant growth as a field of data miningat large. In particular, time-evolving topic discovery, where the evolution ofa topic is taken into account has been instrumental in understanding thehistorical context of an emerging topic in a dynamic corpus. Traditionally,time-evolving topic discovery has focused on this notion of time. However,especially in settings where content is contributed by a community or a crowd,an orthogonal notion of time is the one that pertains to the level of expertiseof the content creator: the more experienced the creator, the more advanced thetopic. In this paper, we propose a novel time-evolving topic discovery methodwhich, in addition to the extracted topics, is able to identify the evolutionof that topic over time, as well as the level of difficulty of that topic, asit is inferred by the level of expertise of its main contributors. Our methodis based on a novel formulation of Constrained Coupled Matrix-TensorFactorization, which adopts constraints well-motivated for, and, as wedemonstrate, are essential for high-quality topic discovery. We qualitativelyevaluate our approach using real data from the Physics and also ProgrammingStack Exchange forum, and we were able to identify topics of varying levels ofdifficulty which can be linked to external events, such as the announcement ofgravitational waves by the LIGO lab in Physics forum. We provide a quantitativeevaluation of our method by conducting a user study where experts were asked tojudge the coherence and quality of the extracted topics. Finally, our proposedmethod has implications for automatic curriculum design using the extractedtopics, where the notion of the level of difficulty is necessary for the propermodeling of prerequisites and advanced concepts.

A Constrained Coupled Matrix-Tensor Factorization for Learning Time-evolving and Emerging Topics