Nonparametric statistical structuring of knowledge systems using binary feature matches

Morten Mørup, Fumiko Kano Glückstad, Tue Herlau, Mikkel N. Schmidt

Abstract: Structuring knowledge systems with binary features is often based on imposing a similarity measure and clustering objects according to this similarity. Unfortunately, such analyses can be heavily influenced by the choice of similarity measure. Furthermore, it is unclear at which level clusters have statistical support and how this approach generalizes to the structuring and alignment of knowledge systems. We propose a non-parametric Bayesian generative model for structuring binary feature data that does not depend on a specific choice of similarity measure. We jointly model all combinations of binary matches and structure the data into groups at the level in which they have statistical support. The model naturally extends to structuring and aligning an arbitrary number of systems. We analyze three datasets on educational concepts and their features and demonstrate how the proposed model can both be used to structure each system separately or to jointly align two or more systems. The proposed method forms a promising new framework for the statistical modeling and alignment of structure across an arbitrary number of systems.