Wse-MF: A weighting-based student exercise matrix factorization model

Students who have been taught new ideas need to develop their skills by carrying out further work in their own time. This often consists of a series of exercises which must be completed. While students can choose exercises themselves from online sources, they will learn more quickly and easily if the exercises are specifically tailored to their needs. A good teacher will always aim to do this, but with the large groups of students who typically take advantage of open online courses, it may not be possible. Exercise prediction, working with large-scale matrix data, is a better way to address this challenge, and a key stage within such prediction is to calculate the probability that a student will answer a given question correctly. Therefore, this paper presents a novel approach called Weighting-based Student Exercise Matrix Factorization (Wse-MF) which combines student learning ability and exercise difficulty as prior weights. In order to learn how to complete the matrix, we apply an iterative optimization method that makes the approach practical for large-scale educational deployment. Compared with eight models in cognitive diagnosis and matrix factorization, our research results suggest that Wse-MF significantly outperforms the state-of-the-art on a range of real-world datasets in both prediction quality and time complexity. Moreover, we find that there is an optimal value of the latent factor K (the inner dimension of the factorization) for each dataset, which is related to the relationship between skills and exercises in that dataset. Similarly, the optimal value of hyperparameter c₀ is linked to the ratio between exercises and students. Taken as a whole, we demonstrate improvements to matrix factorization within the context of educational data.