Matrix and Tensor Factorization for Predicting Student Performance

Abstract

Abstract:Recommender systems are widely used in many areas, especially in e-commerce. Recently, they are also applied in technology enhanced learning such as recommending resources (e.g. papers, books,...) to the learners (students). In this study, we propose using state-of-the-art recommender system techniques for predicting student performance. We introduce and formulate the problem of predicting student performance in the context of recommender systems. We present the matrix factorization methods, known as the most effective recommendation approaches, to implicitly take into account the latent factors, e.g. "slip" and "guess", in predicting student performance. Moreover, the knowledge of the learners has been improved over the time, thus, we propose tensor factorization methods to take the temporal effect into account. Experimental results show that the proposed approaches can improve the prediction results.

Improve the Prediction of Student Performance with Hint's Assistance Based on an Efficient Non-Negative Factorization

“…(3) Positive ia coef: average number of positive elements of ia coef. Matrix T is the partially observed scoring matrix, W ∈ R U×K is a matrix where each row u is a vector containing the K latent factors describing the student u, and H ∈ R K×I is a matrix where each column i is a vector containing the K factors describing the item ("problem-view-step" group) i [1], [2]. So the observed matrix T can be approximately replaced by the multiplication of the matrix W and matrix H, the objective function is:…”

“…According to the investigation of those related works [2], [23], user-item biased can be a good choice for PSP, and it often performs better than MF. Here we compare it with other factorization techniques.…”

“…Where μ is the global average of student scores, b u , and b i is student and item biases respectively [1], [2], [23]. We can simply use stochastic gradient descent to fit the model.…”

“…Some traditional approaches have been utilized in education data mining field. Thai-Nghe et al [2], [24] has utilized the MF to predict student performance on the two datasets from KDD Cup Challenge 2010. They have got good results on the two large datasets.Š.…”