# Graphs Regularized Robust Matrix Factorization and Its Application on Student Grade Prediction
## 4 GRMF Algorithm
\begin{cases}1&0<x<60;\\ 2&60\leq x<70;\\ 3&70\leq x<80;\\ 4&80\leq x<90;\\ 5&90\leq x<100;\\ 6&x=100.\end{cases}  \tag{11}\]

where \(x\) is the score in the grade record while \(y\) is its corresponding grade. Responding to \(\mathbf{M}\in\mathbb{R}^{882\times 15}\), we also removed the student and the course from NPU-S and NPU-C. In all collected side descriptions, we selected 15 and 12 important features for NPU-S and NPU-C, respectively, using teaching experience. Finally, we formulated them into matrices \(\mathbf{S}_{u}\in\mathbb{R}^{882\times 15}\) for students and \(\mathbf{S}_{v}\in\mathbb{R}^{82\times 12}\) for courses. #### Implementation Details

We here predict the student grade for each academic term, because of the usual stages at the university. Hence, we used historical records as a training set to predict the grade in the next term. That is, our model was trained on the records from the 1-th to the \((t-1)\)-th terms and was tested on the \(t\)-th terms. Concretely, in the SGP tasks for the \(t\)-th term, we built \(k\)-nearest neighborhood graph \(\mathbf{G}_{u}/\mathbf{G}_{v}\) on the side data of students and courses \(\mathbf{S}_{u}/\mathbf{S}_{v}\), respectively. Then, we learned the latent features of student and course on training data using our model, followed by computing the evaluation matrix Err1 and Acc. We conduct this experiment on six data splits, where the sizes of training sets and test sets are listed in Table 2.

In order to compare with other methods for SGP, we conducted an experiment using MF ([PERSON], 2010 [46]), NMF ([PERSON], et al., 2015 [22]), PMF ([PERSON], et al. [47]), KNN ( [PERSON], et al., 2019 [48]) and column mean ([PERSON], et al. [49]). Besides, we also implement SGP using RMF-MM ([PERSON], et al., 2018 [26]) and GRALS([PERSON], et al. [29]). For each method, we selected the optimal one from the wide range suggested by their related reports. #### Experimental Result and Discussion

Figure 7(a) and Figure 7(b) show the prediction results from varying all six terms by various methods in terms of Err1 and Acc. From the curves and comparisons, we observe that: (1) as the semester progresses, the prediction decreases in Err1 and increases in accuracy rate; (2) both GRMF and GRALS are better than other comparable methods; (3) GRMF is not only better than RMF but also outperforms GRALS. (4) the prediction performance of colMean can be regarded as a base performance of SGP. Both GRMF and GRALS can perform better than colMean over all the terms while other methods, including the RMF-MM performance are worse than colmean in most cases. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Academic Term** & **Training Set** & **Test Set** \\ \hline
1 & 17,425 & 3189 \\
2 & 20,779 & 2043 \\
3 & 22,821 & 2692 \\
4 & 25,506 & 1473 \\
5 & 26,949 & 2063 \\
6 & 29,045 & 219 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The size of training sets and test sets. From these observations, we derive the following conclusions: (1) As the semester progresses, we obtain more information about the student/course which is reflected in the better prediction performance. (2) Side information data of student and course is helpful for SGP. (3) The combination of the side information and the robust \(L_{1}\) regularizers in our methods GRMF improves the prediction performance effectively. (4) The methods using side information do perform well but other comparable methods cannot handle the prediction task well in the real education context due to the complex problem of real educational data. (5) Our proposed method outperforms traditional classification methods and regression methods. (6) The proposed method GRMF can achieve the accuracy of 65.4% in the sixth term, which is more interesting than the other methods. ## 6 Discussion and Conclusions

In this paper, we solve the student grade prediction (SGP) problem by proposing a novel matrix factorization method that is dubbed GRMF.