# Clustering of LMS Use Strategies with Autoencoders
## 3 Results and Discussion  
As expected, when reducing dimensionality, smaller sizes led to higher reconstruction errors. We empirically found an optimal value for the bottleneck layer that is lower than the dimension obtained from manual data transformation [11]. The autoencoder reduced the input dimension to six features in the latent space, while our previous hand-transformed set consisted of nine variables. As previously mentioned, the defined encoder contains dense layers and the leaky ReLU activation function, and its output layer defines a latent vector size with six nodes. We trained the model for 5000 epochs and calculated the loss and accuracy for each epoch to confirm that it converged. Figure 4 shows loss and accuracy vs. epoch. We can observe that the model converged and how well the autoencoder could reconstruct its input. From the six latent features, we applied K-means to obtain the different clusters. For this, we determined the optimal number of classes. We calculated the silhouette coefficient and gap statistic, obtaining seven as the optimal number of clusters with both methods. Figure 5 shows the seven different clusters after applying K-means from the six latent (hidden) features in a 2D space. Once the seven clusters were obtained, we analyzed them to interpretate the obtained results. For this purpose, we studied these seven classes in relation to the users' activity variables described in Table 1, and we checked if it was possible to define a course typology based on these results. Figures 6 and 7 show the normalized mean value of the variables associated with the teachers' and students' activity, respectively. From these results, seven different course typologies were established. Class 2 corresponds to courses with low use of Moodle or inactive courses (type I or Inactive). Class 6 corresponds to courses whose main activities are students viewing content and teachers sending announcements to the forum. In these courses, teachers use the platform as an informative medium or a Web repository (type R or Repository). Classes 3, 4 and 7 are courses with static content and the use of evaluation based on task assignments. The main difference is that Class 3 matches courses that also have a high use of discussion forums and teacher-student communication, showing a more communicative profile (type C or Communicative). Class 4 has a greater use of assignments and evaluative elements such as manual gradebook items (type E or Evalative). Class 7, in turn, has a high number of entries in the calendar and in the gradebook; this suggests that the teachers use Moodle as an organizing element and class planner (type P or Planner). On the other hand, Class 1 corresponds to courses with a mixed use of Moodle tools; these are courses with large amounts of content, forums and assignments, combined with quizzes and evaluative elements (type B or Balanced). Finally, Class 5 consists of courses with very high and wide use of all types of activities on Moodle, including advanced activities (type V or adVanced). Table 2 shows a summary of the seven course typologies described previously, indicating their main features. At first, we can observe that these seven classes are similar to the six typologies defined in our previous study [11], although some types have disappeared (like Submission -S) and there are new types. Our aim is to see if there is any connection between them. Figure 8 represents a mosaic plot, where we can visually compare the different groups and obtain a general idea of how they are related to each other. We can observe that the adVanced courses were previously classified as B because the variable associated with advanced activities had been eliminated in the preprocessing of the data, since it was zero in most  
Figure 4: Loss and accuracy vs. epoch. Figure 5: Two-dimensional K-means clustering (k = 7) from latent features (hid1 to hid6). courses.