# Graph Neural Network for Senior High Student's Grade Prediction
## 3 Experiments
The predicted rank of geography is 41, but the real rank is 42. The relative error is \(-1/13\) (i.e., \((12-13)/13\)), \(1/15\), and \(-1/42\), respectively. For the whole \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Date** & **Maths Grade \& Rank** & **English Grade \& Rank** & \\ \hline
2017/04/20 & 79 \& 24 & 76 \& 34 & \\
2017/04/21 & 79 \& 24 & 76 \& 34 & \\
2017/04/22 & 79 \& 24 & 76 \& 34 & \\ \hline  & & & & \\
2018/02/18 & 91 \& 04 & 72 \& 35 & \\ \hline  & & & & \\
2018/11/04 & 86 \& 12 & 79 \& 27 & \\
2018/11/05 & 86 \& 13 & 79 \& 27 & \\ \hline \hline \end{tabular} Extended data along the **date** axis.  
\end{table} 
Table 4: Extended Examination Data of Student 14295. Figure 9: The curve of loss function in the data from nine examinations. subjects prediction, only one subject (geography) grade and three subject ranks (maths, chemistry, and geography) are not predicted precisely. The relative error of subject grade prediction is \(1/10\) (total 10 subjects). The relative error of subject rank prediction is \(3/10\). Finally, it can be seen that, with enough data, the graph neural network performs well in the personalized grade prediction. In fact, only the node attribute (tensor of subject grade and rank) is presented in Table 5 to show the performance of the graph neural network based personalized grade prediction model. The global attribute (tensor of total grade and average rank) is also predicted. The predicted total grade is (742.4492 (floating-point), 743 (ceil)), and the real total grade is 743. The predicted average rank is (27.1625 (floating-point), 28 (ceil)), and the real average rank is 27. Similarly, the edge attribute (tensor of the ratio of the receiver node attribute to the sender node attribute, which has 90 elements, so it is not presented without causing confusion) can be easily obtained and compared. Besides, linear regression (LR) [11; 12; 21], support vector regression (SVR) [23; 31], and multi-layer perceptron (MLP) neural network [27; 29; 31] are compared to the proposed model. The training dataset, validation dataset, and testing dataset are the same as the proposed model. The corresponding hyperparameters are as follows. For SVR, the radial basis function, which is the most common kernel function, is selected. The MLP contains two hidden layers. Each of the hidden layers has 16 neurons (nodes). The Adam optimization method is employed to train the MLP. The learning rate is set to be 0.02. The mean absolute percentage error (MAPE) is used to evaluate the prediction performances. For the student 14295, the prediction performances of the different methods are compared and presented in Table 6. It can be seen that the proposed prediction model has the best performance for predicting the grades and ranks of the student 14295. Figure 10: The curve of loss function in extended data. \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Subject** & \(\mathbf{grade}\)**(Float, Ceil)** & **Grade** & \(\mathbf{rank}\)**(Float, Ceil)** & **Rank** \\ \hline Chinese & (80.2998, 81) & 81 & (22.9532, 23) & 23 \\ Maths & (85.2500, 86) & 86 & **(11.8778, 12)** & **13** \\ English & (78.3439, 79) & 79 & (26.9669, 27) & 27 \\ Physics & (85.9123, 86) & 86 & (10.8730, 11) & 11 \\ Chemistry & (83.3443, 84) & 84 & (**15.5037, 16**) & **15** \\ Biology & (74.4902, 75) & 75 & (32.8843, 33) & 33 \\ Politics & (66.8594, 67) & 67 & (40.9425, 41) & 41 \\ History & (63.3881, 64) & 64 & (41.8732, 42) & 42 \\ Geography & **(46.1224, 47)** & **46** & **(40.9427, 41)** & **42** \\ Technology & (78.4384, 79) & 79 & (26.8082, 27) & 27 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Prediction Performance of Proposed Method. Additionally, considering the generality, we extend the experiment to 100 students randomly selected from the dataset of Ningbo Xiaoshi High School, to investigate the performance of the proposed method on a relatively large dataset. The other comparing methods (i.e., LR, SVR, and MLP) are also carried out to compare with the proposed method.