## 3 Experimental Design
### Cluster Analysis
#### 3.3.2 Analysis of Clustering Results  
The optimal number of clusters and initial cluster centroids were determined and used as inputs for the K-means algorithm. K-means was then executed to iteratively refine the clustering within each canopy cluster, ensuring an accurate grouping. At the conclusion of the iterations, the clustering results were analyzed, revealing that the female group could be categorized into four distinct clusters, while the male group was divided into three clusters. Each cluster exhibited unique characteristics across various physical fitness test indicators. The clustering outcomes and visualizations are presented using 3D scatter plots, as shown in Figures 16 and 17, effectively illustrating the distribution and differences among clusters. Figure 16: Visualization of the clustering results of the improved canopy-K-means algorithm based on Principal Component Analysis (PCA) for the male group. Figure 15: Results of the feature importance analysis for female group characteristics using three tree-based algorithms. The specific results are analyzed in the following tables. The final clustering results of the boys' group are detailed in Table 3, and the final clustering results of the girls' group are detailed in Table 4. Tables 3 and 4 present the results of K-means clustering for male and female student groups, respectively. Each numerical value in the tables represents the mean score of a specific physical fitness indicator within the corresponding cluster. For instance, in Table 3, Cluster 1 of the male group (\(n\) = 4342) shows relatively balanced performance across all items, with moderate scores in both endurance (1000 m running score: 70.73) and strength (pull-up score: 68.75). In contrast, Cluster 2 (\(n\) = 1930) demonstrates a sharp decline in endurance (1000 m running score: 12.73), despite slightly better scores in flexibility and explosive strength. This suggests the existence of a subgroup that may require targeted cardiovascular or aerobic capacity training. \begin{table}
\begin{tabular}{c c c c} \hline
**Cluster** & **Cluster 1** & **Cluster 2** & **Cluster 3** \\ \hline Amount & 4342 & 1930 & 4384 \\ BMI Score & 97.34 & 95.82 & 94.42 \\ Lung Capacity Score & 73.51 & 74.30 & 74.38 \\
50 m Running Score & 79.19 & 70.30 & 74.00 \\ Standing Long Jump Score & 75.30 & 78.40 & 61.00 \\ Sitting Forward Bend Score & 75.36 & 71.82 & 70.01 \\
1000 m Running Score & 70.73 & 12.73 & 59.14 \\ Pulling up Score & 68.75 & 53.71 & 7.99 \\ Health results & 77.17 & 65.30 & 63.00 \\ \hline \end{tabular}
\end{table} 
Table 3: K-means clustering results for the male group. Figure 17: Visualization of the clustering results of the improved canopy-K-means algorithm based on Principal Component Analysis (PCA) for the female group. Similarly, in the female group shown in Table 4, Cluster 3 (\(n\) = 4379) consistently achieves the highest average scores across nearly all indicators, including BMI (98.95), standing long jump (83.70), and overall health results (80.76), suggesting a high-performing cohort. Conversely, Cluster 2 (\(n\) = 1771) reveals a significant deficiency in core strength, as reflected by a low sit-up score (17.65), despite average performance in other areas. These cluster-specific profiles not only reflect differences in physical health status among students but also highlight the necessity for customized training or intervention programs. By identifying these distinct group characteristics, educational institutions can more effectively allocate resources and design targeted fitness programs to address the unique needs of each subgroup. The radar chart of the physical fitness test for male and  
As shown in Tables 3 and 4, along with Figures 18 and 19, the male students are categorized into three distinct clusters, while the female students are grouped into four clusters. Each cluster demonstrates unique performance characteristics across various physical fitness indicators. 1.