# Graphs Regularized Robust Matrix Factorization and Its Application on Student Grade Prediction
## 1 Introduction  
In high school education, student grade prediction (SGP) can make great sense for aiding all stakeholders in the education process. For students, SGP can help them to choose suitable courses or exercises for increasing their knowledge, and even to make their pre-plans for academic periods. For instructors, SGP can help them to adjust learning materials and teaching programs based on student ability, and to find the students that are at risk of disqualification in course progress. For educational managers, SGP can help them to check the curriculum program and to arrange the courses in a scientific order. All stakeholders of the educational process could have a better self-plan to improve education outcomes and then have a higher graduation rate. SGP is an important problem for scientific education in STEM (Science, Technology, Engineering, Mathematics), referred to in the work of [PERSON] et al. [1]. Student grade prediction aims to predict the final score/grade of course enrolled by a target student in the next academic term. SGP provides a useful reference to evaluate educational outputs in advance and is thus significant necessary for various tasks towards personalized education, such as ensuring on-time graduation [2] and improving learning grade [3; 4]. Over the past years, many studies have paid attention to SGP and have already developed many methods [5]. Existing methods can be principally divided into three categories depending on their formulation, as follows: (1) Classification problem. SGP is recast as labeling the target student with the predefined grade tags and was solved by classification models, such as decision tree [6], logic regression [7; 8] and support vector machine [9; 10]. (2) Regression problem. By taking the grade as the response variable, SGP is rewritten into assigning scores following the features of student or course, such as linear regression [5; 11; 12], neural network [13; 14; 15] and random forest [9]. (3) Matrix completion. Since grade records can be poured into a matrix, SGP is also formulated as predicting the missing values of the student-course matrix with each element being a course grade [16]. This formulation is usually solved by the popular method of matrix factorization and has been extensively studied, leading to many effective approaches [17; 18]. In particular, based on the same dataset, [PERSON] et al. compared matrix competition with traditional regression methods such as logistic/linear regression and the experimental results show that matrix competition can improve prediction results [19]. MF based methods aim to learn the latent features of student and course from the given grade data and then uses these features for SGP [20]. Here, we review the related works that using MF techniques. Traditional MF was employed to implicitly encode \"slip rate\" (the probability that the student knows how to solve a question but makes a mistake) and the \"guess rate\" (the probability that the student does not know how to solve a question but guesses correctly) of the student in an examination, resulting in an excellent performance on the educational data set of KDD (Knowledge Discovery and Data Mining) Cup 2010 [21]. In References [22; 23], Non-negative Matrix Factorization (NMF) was used to integrate the nonnegativity of student grade. Tensor factorization (TF) was exploited to take the temporal effects into account in Reference [24], due to the improvement of the ability of students. Since grade matrix is implicitly low rank, low-rank matrix factorization (LRMF) was investigated in data sets from the online learning platform in the work of [PERSON] et al. [25]. But the existing MF based methods often suffer from the issues of missing data, corrupted data, and data noise. Especially, they fail to consider the side information which is included in the other handy educational data, such as background data and daily behavior data in school. Since the \(L_{2}\)-norm based reconstruction is sensitive to outliers and data corruptions, [PERSON] et al.