## 2 Drone Clustering Based on the K-Means++ Algorithm
### Analysis of Experimental Results  
In this paper, 50 UAVs were selected as experimental samples, covering UAV models widely used in low-altitude scenarios. A total of 100 iterations were performed under different numbers of clustering centers, aiming to explore and verify the robustness and optimal configuration of the clustering effect through a large-scale experimental design. The clustering results were quantitatively evaluated using three key evaluation metrics, namely, contour coefficient, sum of squared errors, and Davidson-Bourdain index, and in terms of multiple dimensions, such as compactness within clusters, separation between clusters, and relative positions of samples in the clusters to which they belong, thus enabling systematic comparisons of differences in effectiveness under different numbers of clustering centers. The results of the performance-based UAV clustering evaluation index are shown in Table 1.  
Based on the analysis of the clustering evaluation indexes in the table, it can be seen that when the K value was set to 4, the profile coefficient was closest to the ideal value of 1, which indicated that at this time the clustering structure was the clearest, the separation between clusters was the greatest, and the clustering effect reached the best state; when the K value was 3, the sum of squares of the error was the minimum, which indicates that in the process of dimensionality reduction and reconstruction of the data, the loss of information was minimized, and the accuracy of the clustering was the highest; and when the K value was 15, the Davidson-Bourdain index was closest to 0, which means that the homogeneity within the clusters was excellent and the differences between the clusters were significant, also showing good clustering performance. However, the optimization of a single index did not fully represent the optimization of the clustering effect. Therefore, it was necessary to comprehensively consider the trend of the clustering indicators under different K values to find a balance point, so that the clustering effect was both interpretable and relatively ideal. Figure 2 graphically shows the dynamic curve of these indicators with the change in K value. The analysis of these curves  
\begin{table}
\begin{tabular}{c c c c} \hline
**K** & **Sil** & **SSE** & **DBI** \\
**(The Number of Clusters)** & **(Silhouette Coefficient)** & **(Sum of Squared Errors)** & **(Davies–Bouldin Index)** \\ \hline
2 & 0.43874 & 3.1606 & 4.0803 \\
3 & 0.57906 & 0.93635 & 1.64545 \\
4 & 0.82198 & 0.94477 & 0.48692 \\
5 & 0.78518 & 1.31299 & 0.4326 \\
6 & 0.69245  
was used to more accurately determine a more appropriate K value, in order to achieve the optimization goal of clustering analysis. In Figure 2a, when the K value was raised from 2 to 4, it is observed that the profile coefficient Sil was significantly elevated, which indicates that the groups formed by clustering showed a higher degree of differentiation among themselves. Following this, when the K-value was gradually increased from 4 to 16, the Sil value showed a decreasing trend, but this decreasing rate slowed down significantly. Combined with the change in Sil value and K-value, we can judge that when the K-value was set to 4, the separation between the clustered groups reached the optimal state; in Figure 2b, the error squared and the SSE reached their lowest points when the K-value was set to 3, which indicates that, at this time, the accuracy of the data clustering was the highest, with the increase in K value. Although the SSE value had some ups and downs, the overall trend tended to grow. It is worth noting that, in the process of the K value increasing from 3 to 4, the rate of increase in SSE slowed down significantly. Thus, using the SSE as an evaluation index, it can be assumed that for a K value between 3 and 4, the clustering effects presented are more ideal. From Figure 2c of the Davidson-Bourdain index curve trend, it can be seen that with the increase in K value, the clustering effect presented was more ideal.