Data Preprocessing with IRM for skill extraction using NMF

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To provide examinees with appropriate question items, identifying and evaluating users' latent and acquired skills is important in e-learning systems. These latent skills are defined in terms of a Q-matrix. Constructing Q-matrices manually is relatively labor-intensive, because doing so requires expert insight as well as verbal examination to identify which skills students have mastered. Methods to extract a Q-matrix from examination results automatically using nonnegative matrix factorization (NMF) have been explored, and improved methods such as online NMF have been proposed, which extracts an immutable Q-matrix from time-series data. In this study, we propose a data preprocessing method to improve the accuracy of NMF using a co-clustering method called an infinite relational model (IRM). We also describe experiments conducted using synthetic data, in which learners' skills and the bias in the number of their responses were evaluated, and show that the results demonstrate the efficacy of the proposed approach.