## 5 Experiments
### Experimental Results
#### 5.4.1 Comparison Experiments with Different Overlap Rates  
First, comparative experiments were conducted on noise-free data with initial structure overlap rates of 20%, 40%, and 60%. The test set contained 100 pairs of graphs. The registration results are shown in Tables 3-5, demonstrating the performance comparison between our method and other similar methods. The experimental results indicate that our method achieved the best performance, surpassing other comparative methods. Our method was compared with several traditional and popular graph neural network algorithms. The experimental results demonstrate that EKNet outperforms other graph neural learning-based algorithms across multiple metrics. Specifically, our algorithm achieves a Mean Squared Error (MSE) in Euler angle rotation that is two orders of magnitude lower than the commonly used GCN algorithm and one order of magnitude lowerthan the second-best GraphKAN method, resulting in a 94.98% improvement. The unit related to translation error is meters. In terms of translation vector error MSE(t), EKNet significantly outperforms the SGC algorithm and is one order of magnitude better than the GDC algorithm. EKNet requires a floating-point operation volume of 171.50 M and has a parameter count of only 3.166 K.  
This significant performance improvement is primarily attributed to the feature construction module, which accurately extracts features, and the node feature matching module, which plays a crucial role in the registration process. From the tables above, it is evident that there are significant differences in registration time among different algorithms. For example, the GAT algorithm, due to its high computational complexity, runs slowly, requiring 164 s to register 100 pairs of graphs with an overlap rate of 60%. In contrast, the GCN algorithm, with its simpler structure, runs faster but does not achieve the best registration results. Moreover, as the overlap rate decreases, the error increases for all methods, further demonstrating the advantage of our feature construction module in extracting precise features and the importance of the node feature matching module in the registration process. The experimental results prove that EKNet can effectively handle the registration of partially overlapping point clouds and outperforms some popular registration algorithms in terms of performance. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Method** & **RMSE(R)** & **RMSE(t)** & **MAE(R)** & **MAE(t)** & **Times(s)** \\ \hline GDC [53] & 0.051 & 0.302 & 0.018 & 0.126 & 17.5 \\ GAT [44] & 0.104 & 0.909 & 0.036 & 0.273 & 168.4 \\ GCN [21] & 0.045 & 0.316 & 0.011 & 0.074 & 21.9 \\ GraphKan [50] & 0.023 & 0.173 & 0.011 & 0.083 & 24.2 \\ SGC [54] & 0.244 & 1.842 & 0.116 & 0.855 & 27.8 \\ NIGCN [55] & 0.126 & 1.043 & 0.066 & 0.513 & 28.1 \\ Ours & 0.005 & 0.037 & 0.002 & 0.017 & 18.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Registration performance at 40% overlap. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Method** & **RMSE(R)** & **RMSE(t)** & **MAE(R)** & **MAE(t)** & **Times(s)** \\ \hline GDC [53] & 0.158 & 1.080 & 0.085 & 0.554 & 17.8 \\ GAT [44] & 0.245 & 1.673 & 0.144 & 0.937 & 168.3 \\ GCN [21] & 0.176 & 1.238 & 0.092 & 0.610 & 17.4 \\ GraphKan [50] & 0.103 & 0.719 & 0.054 & 0.349 & 20.2 \\ SGC [54] & 0.451 & 3.286 & 0.280 & 1.971 & 21.9 \\ NIGCN [55] & 0.368 & 2.713 & 0.233 & 1.664 & 30.5 \\ Ours & 0.030 & 0.193 & 0.010 & 0.067 & 12.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Registration performance at 20% overlap.