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 ex-ercises 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 Ex-ercise 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 c 0 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. (c) 2023 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/ )

Automated summary

Students can develop their skills by completing a series of tailored exercises, which is more effective than choosing exercises from online sources themselves. This paper presents a novel approach called Weighting-based Student Exercise Matrix Factorization (Wse-MF) that combines student learning ability and exercise difficulty. The research results demonstrate that Wse-MF outperforms other models in cognitive diagnosis and matrix factorization in terms of prediction quality and time complexity. There is also an optimal value of the latent factor K and hyperparameter c0 for each dataset. Overall, this paper contributes to the improvement of matrix factorization in educational data.