# Optimizing Latent Factors and Collaborative Filtering for Students' Performance Prediction
## 5 Experimental Results
### Datasets  
We built several datasets to perform the experiments of predicting students' performance. They are available at the Mendeley Data repository [46]. These datasets were prepared from virtual classrooms of a series of university-level courses, the data of which were adequately filtered according to the method explained in Section 3.3. The purpose of preparing this suite of datasets was having different cases for different academic contexts: number of students and tasks, degree levels (first, middle, or final years), academic nature (theoretical or practical contents), etc. This heterogeneous suite also contributes to considering a different number of latent factors, which is important in order to test the optimization algorithms proposed in Section 4. The virtual classrooms of the online campus of the University of Extremadura (UEX) provided the necessary data for the datasets. This online campus is composed of several software services working together in order to cater to the needs of the users:  
* Portal: It welcomes users and allows them to log in. It also implements the only communication channel between the users and tech support. * Avuex: It consists of a large set of virtual classrooms corresponding to the different bachelor's and master's degrees, oriented toward the learning process. * Evuex: It consists of a set of virtual spaces oriented toward different purposes for the university community (short courses, seminars, workshops, etc.). Table 2 shows the datasets corresponding to eight virtual classrooms. It lists the number of students (\(S\)), tasks (\(I\)), the performance matrix (\(P\)) before (original data) and after (filtered data)  
Figure 5: GAK method: combination of a \(K\) loop and GA for optimizing the pair (\(\beta\),\(\lambda\)). the filtering process, the number of known (\(D^{train}\)) and unknown (\(D^{tunk}\)) performances, the sizes of the training (\(D^{traint}\)) and test (\(D^{test}\)) datasets, and the percentages of the minimum activity levels for students and tasks allowed by the filtering method. Besides, we can see in Figure 6 the variety of shapes and of the eight datasets. The number and location of the unknown performances are highlighted. This variety of features allows the algorithms to demonstrate their effectiveness in different scenarios. \begin{table}
\begin{tabular}{l l l l l l l l l} \hline \hline
**Dataset** & **IC** & **HS** & **TO** & **EN** & **BE** & **PR** & **SR** & **SJ** \\ \hline
**Virtual** & **Introduction** & **Food Hygiene** & **Clinical** & **Women’s** & **Biostatistics for** & **Internet** & **Network** & **Youth** \\
**Classroom** & **to Computers** & **and Safety** & **Toxicology** & **Nursing** & **Biotechnology** & **Programming** & **Security** & **Subcultures** \\ \hline \multirow{2}{*}{\(S\) (students) \(I\) (tasks)} & Original data & & & & & & & \\  & 207 & 128 & 123 & 90 & 47 & 78 & 17 & 26 \\  & 38 & 16 & 6 & 18 & 30 & 17 & 24 & 6 \\  & 7866 & 2048 & 738 & 1620 & 1410 & 1326 & 408 & 156 \\ \hline \multirow{2}{*}{\(S\) (students) \(I\) (tasks)} & Filtered data & & & & & & & \\  & 107 & 95 & 116 & 78 & 47 & 65 & 10 & 26 \\  & 8 & 5 & 3 & 9 & 10 & 2 & 24 & 6 \\  & 7856 & 475 & 348 & 702 & 470 & 130 & 240 & 156 \\ \hline \multirow{2}{*}{\(D^{tunk}\) (known data)} & Subsets & & & & & & & \\  & 800 & 457 & 324 & 657 & 440 & 116 & 214 & 155 \\  & 56 & 18 & 24 & 45 & 30 & 14 & 26 & 1 \\  & 800 & 457 & 324 & 657 & 440 & 116 & 214 & 155 \\  & 102 & 92 & 105 & 73 & 43 & 59 & 19 & 26 \\ \hline \multicolumn{7}{c}{Minimum activity level} \\ Students’ & 88\% & 60\% & 33\% & 78\% & 30\% & 50\% & 50\% & 83\% \\ Tasks’ & 80\% & 92\% & 86\% & 77\% & 89\% & 78\% & 75\% & 96\% \\ \hline \multicolumn{7}{c}{\({}^{1}\) Greater than or equal to 25\%, \({}^{2}\) Greater than or equal to 75\%.} \\ \end{tabular}
\end{table} 
Table 2: Experimental datasets. Figure 6: A variety of the characteristics of the datasets. The unknown performances are highlighted. Table 3 shows the optimal values found after applying the GAK method.