## 4 Experiment and Results
### Results
With three clients, the silhouette score consistently shows values close to 0.8, indicating high data aggregation within clusters and clear boundaries between clusters. With five clients, the silhouette score varies between 0.7 and 0.85, with more clients with unclear cluster boundaries than with three clients. With 10 clients, the silhouette score falls below 0.7 on average, indicating that the boundaries between clusters are more blurred, and clustering efficiency tends to decrease as the number of clients increases. Looking at accuracy, with three clients, the accuracy ranges between 93% and 97%, indicating that the small number of clients means that the amount of data covered by each client is sufficient and the learning performance is stable. With five clients, the accuracy varies from 88% to 97%, with some clients performing below 90%, which is likely due to data imbalance or distributed learning. With 10 clients, the accuracy variance is wider, ranging from 85% to 95%, indicating that the difference in performance is due to the size and quality of the data each client handles. In terms of convergence speed and learning stability, the convergence speed is relatively fast with three clients. When converged models from each client are merged, performance does not degrade significantly and optimization is stable. With five clients, convergence can be a bit slower, and the difference in model performance between clients can be large. With 10 clients, convergence is even slower, and the model gap between clients becomes larger, making learning less stable. This is because synchronization becomes more difficult and the optimization process becomes more complex. In conclusion, three clients provides overall stable results in performance metrics such as NMI, silhouette score, and accuracy. It is also very favorable in terms of convergence speed and communication efficiency. On the other hand, as the number of clients increases to 5 and 10, the performance variance tends to increase, the clustering quality decreases, and the communication and computational resource consumption increases. Therefore, three clients is the optimal setting for balancing resource efficiency and performance. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Round** & **Client 1** & **Client 2** & **Client 3** & **Client 4** & **Client 5** & **Client 6** & **Client 7** & **Client 8** & **Client 9** & **Client 10** \\ \hline
0 & 0.554 & 0.448 & 0.639 & 0.573 & 0.565 & 0.561 & 0.459 & 0.462 & 0.574 & 0.647 \\
1 & 0.710 & 0.650 & 0.755 & 0.736 & 0.728 & 0.721 & 0.659 & 0.662 & 0.737 & 0.764 \\
2 & 0.766 & 0.724 & 0.798 & 0.789 & 0.784 & 0.778 & 0.731 & 0.737 & 0.791 & 0.807 \\
3 & 0.802 & 0.769 & 0.827 & 0.829 & 0.819 & 0.814 & 0.773 & 0.777 & 0.829 & 0.834 \\
4 & 0.832 & 0.801 & 0.847 & 0.858 & 0.844 & 0.838 & 0.803 & 0.806 & 0.855 & 0.852 \\
5 & 0.850 & 0.825 & 0.857 & 0.876 & 0.857 & 0.853 & 0.826 & 0.827 & 0.874 & 0.862 \\
6 & 0.861 & 0.842 & 0.859 & 0.890 & 0.867 & 0.865 & 0.840 & 0.843 & 0.887 & 0.866 \\
7 & 0.868 & 0.851 & 0.863 & 0.897 & 0.873 & 0.874 & 0.851 & 0.850 & 0.897 & 0.869 \\
8 & 0.874 & 0.860 & 0.865 & 0.902 & 0.879 & 0.880 & 0.860 & 0.860 & 0.902 & 0.875 \\
9 & 0.871 & 0.865 & 0.860 & 0.901 & 0.875 & 0.876 & 0.860 & 0.862 & 0.902 & 0.871 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Silhouette scores of each client over epochs. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Round** & **Server** & **Client 1** & **Client 2** & **Client 3** & **Client 4** & **Client 5** & **Client 6** & **Client 7** & **Client 8** & **Client 9** & **Client10** \\ \hline
0 & 0.9997 & 0.965 & 0.936 & 0.976 & 0.976 & 0.968 & 0.970 & 0.961 & 0.950 & 0.940 & 0.930 \\
1 & 0.991 & 0.953 & 0.922 & 0.968 & 0.973 & 0.963 & 0.968 & 0.956 & 0.945 & 0.935 & 0.925 \\
2 & 0.9977 & 0.952 &Figure 12 graphs the NMI values of each client over the round, and Figure 13 graphs the silhouette score values of each client over the rounds. Figure 14 graphs the values of the server and each client over the rounds.