# Clustering Analysis for Classifying Student Academic Performance in Higher Education
## 4 Experimental Results and Analysis  
### Internal Validation  
This section demonstrates the clustering results obtained using the proposed method. Indicators that should be given attention when checking the scores of clustering evaluation metrics are as follows: low DB index values; silhouette coefficient index with a high positive value; and the CH index with high values shows good clustering achievement. Table 8 summarizes the results of clustering performance based on internal validation for three clustering algorithms, k-means, BIRCH, and DBSCAN, applied to three different model types: Model A, Model B, and Model C. The algorithm's running time to execute is also given in the table.  
Table 9 summarizes clustering performance based on the internal validation of three clustering algorithms, k-means, BIRCH, and DBSCAN, applied to three models: Model A,  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline
**Algorithm** & \multicolumn{4}{c}{**Model A**} & \multicolumn{4}{c}{**Model B**} & \multicolumn{4}{c}{**Model C**} \\ \cline{2-13}  & **DB** & **Silhouette** & **CH** & \begin{tabular}{c} **Time** \\ **(s)** \\ \end{tabular} & **DB** & **Silhouette** & **CH** & \
\begin{tabular}{c} **Time** \\ **(s)** \\ \end{tabular} & **DB** & **Silhouette** & **CH** &
\begin{tabular}{c} **Time** \\ **(s)** \\ \end{tabular} \\ \hline k-means & 1.85 & 0.18 & 20,846.33 & 238 & 1.71 & 0.192 & 24,946.34 & 238 & 1.891 & 0.16 & 17,358.46 & 231 \\ BIRCH & 2.08 & 0.14 & 17,203.63 & 254 & 1.96 & 0.165 & 21,722.28 & 223 & 2.222 & 0.12 & 14,664.02 & 235 \\ DBSCAN & 1.43 & \(-\)0.17 & 3034.38 & 269 & 2.08 & 0.082 & 11,218.19 & 306 & 2.229 & \(-\)0.02 & 6760.80 & 308 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Result of clustering model evaluation.  
Based on the results of clustering performance in Table 8, each algorithm is ranked to identify its performance. Table 9 shows the list of ranks for each algorithm based on the mean score of DB, silhouette, and CH. For example, the k-means algorithm for Model B is given the first rank because after comparing it with other models, its DB has the lowest value, the silhouette has the highest value, and the CH has the highest value. Model B recorded the best mean score of 4, followed by Model A with a score of 6 and Model C with a total score of 8. Hence, Model B is the best model compared to the other two based on the table above.  
From the comparison between all of the models above, we will focus on the evaluation analysis of the three clustering algorithms used in Model B because it was better than Model A and C. Table 8 shows the DB index, silhouette coefficient index, and CH index clearly show the k-means dominance over the other two algorithms. The DB index value for the k-means is 1.71, which is lower than BIRCH (1.96) and DBSCAN (2.08). For the silhouette index, k-means again recorded the best result where the value is the highest (0.192) as compared to BIRCH (0.165) and DBSCAN (0.082). Meanwhile, for the CH index, values recorded by all three algorithms are 24946.34 for k-means, the highest, followed by 21722.28 for BIRCH and 11218.19 for DBSCAN. So, based on the internal validation evaluation, the k-means algorithm was the best for Model B.  
The silhouette plot in Figure 4 shows that all five clusters generated by the BIRCH algorithm are above the silhouette average value line and show good clustering results. The mean value of the Model B silhouette coefficient index for the BIRCH algorithm is 0.165 and is shown on the plot with a red dotted line. Compared to the k-means, the silhouette coefficient value of the BIRCH algorithm decreased by 0.027. Plot size fluctuations showed  
Figure 4: Clusters silhouette plot for BIRCH Model B.  
Figure 3: Clusters silhouette plot for k-means Model B (KMoB).  
large and significant changes where small sizes were indicated by clusters 1, 2, and 4 while large sizes were indicated by clusters 0 and 3.