Improving matrix factorization techniques of student test data with partial order constraints

• Authors: Behzad Beheshti;Michel Desmarais
• Venue: UMAP'12 Proceedings of the 20th international conference on User Modeling, Adaptation, and Personalization
• Year: 2012

Matrix factorization is a general technique that can extract latent factors from data. Recent studies applied matrix factorization to the problem of establishing which skills are required by question items, and for assessing student skills mastery from student performance data. A number of generic algorithms, such as Non-negative Matrix Factorization and Tensor factorization, are used in these studies to perform the factorization, but few have looked at optimizing these algorithms to the specific characteristics of student performance data. In this thesis, we explore how one such characteristic can lead to better factorization: the fact that items are learnt in a constrained order and allow such inferences as if a difficult item is succeeded, an easier one should also be succeeded. In particular, we want to address this question: can a partial order knowledge structure (POKS) be used to guide matrix factorization algorithms and lead to faster or better solutions to latent skills modelling?