## 4 Experiments and Results
### Clustering: Top Feature Importance  
We utilized all the features in the clustering analysis presented in Section 4.4. In this section, we evaluate how much clustering changes when we use a subset of the features, leveraging the feature importance analysis from Section 4.3. For each classification method used in the binary prediction (LR, RF, and SVM) and each \(\text{CWA}_{U}\) (20%, 40%, 60%, and 80%), we selected the top 5 most important features. We then identified the features that appeared most frequently. Finally, the following five features emerged as the most significant for the analysis: mean_simulations_attempt, mean_simulations_time, mean_workshops_attempt, mean_workshops_time, and weighted_average. The Elbow and Silhouette analyses using these features indicate that the optimal \(k\) value is \(k=5\) at 20% and 60% \(\text{CWA}_{U}\) and \(k=4\) at 40% and 80% \(\text{CWA}_{U}\). We selected \(k=4\) for k-means clustering across all \(\text{CWA}_{U}\) thresholds to guide our analysis for consistency and better interpretation.  
Table 10 shows the centroids of all features used for the clustering analysis. Each cluster contains more similar samples across all \(\text{CWA}_{U}\) thresholds.  
The following general patterns were observed across all thresholds:  
1. Students in clusters who engage intensively with simulations and workshops tend to have higher weighted averages, indicating better performance.
2. Clusters with fewer students often show more focused and efficient study habits, achieving higher weighted averages despite lower overall engagement.
3. The balance and variation in study habits play a crucial role in academic performance, as evidenced by the higher weighted averages of students who manage their study time effectively across different resources.  
We also ran ANOVA tests, showing that such a relationship exists (\(p\)-value \(<0.05\)). Then, we conducted [PERSON]'s post hoc tests to see if there were significant differences in student performance for each pair of clusters.  
The consistent significant \(p\)-value in the post hoc analysis highlights the strength of the clustering approach in identifying distinct groups of students based on their behavior and performance patterns (as we can see from Figure 14 and Table 11, where the clustering results are more distinguishable than the saw in Section 4.5). This insight can help design targeted educational strategies and support mechanisms to enhance student success. Our main conclusions are that higher engagement in simulations and workshops corresponds to better academic outcomes, and the distinct clusters represent different levels of student performance and engagement. These findings underline the importance of active participation in simulations and workshops, which can inform targeted interventions to support students effectively.  
Additionally, analyzing the top features improves clustering by increasing the number of paired clusters with significant differences compared to clustering with all features,leading to more meaningful insights into student performance patterns. However, despite these improvements, our analysis of the Linearity Score using top features revealed no clear relationship between linearity and weighted average. This suggests that the selected feature set may not fully capture the factors influencing a student's navigation path.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**CWA\({}_{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{ \