Student knowledge diagnosis on response data via the model of sparse factor learning

Cognitive diagnosis aims to analyze the status of knowledge mastery of student and is thus very important for personalized education. The existing methods mostly depend on the empirical Q-matrix from domain experts. However, the knowledge points in Q-matrix are unavoidably overlapping, leading to the weak performance on the practical applications. In this paper, we propose a novel model for student knowledge diagnosis, called Sparse Factor Learning (SFL). SFL learns a meta-knowledge dictionary from student response data of test questions, where the knowledge structure of any entity (e.g., student, question or others) is a sparse linear combination of dictionary atoms. Our method has three innovations for cognitive diagnosis: learning latent nonoverlapping meta-knowledge, sparely representing the entities, and removing the bias noise for guessing and slipping. To verify our method, we collected the response data from the final exam of C language program of international class and then conducted the experiments for knowledge diagnosis, student grouping and response prediction. The experiment results show that SFL works effectively and results in decent performance. Besides, it delivers that student who favors mathematics and physics can achieve higher score. All codes and data set can be available on our website.