## 4 Experiments
### Model Training and Performance Comparison  
An evaluation of link prediction performance was conducted to assess the effectiveness of DBGNN on the bubble diagram link prediction task. Several baseline models, including GCN, GAT, and GraphSAGE, are selected for comparison. GCN is constructed based on the node's spatial relations, propagating node information along edges [41]. GAT introduces the attention mechanism to learn the relative weights between two connected nodes because it has greater expressive capability. GraphSAGE is an inductive learning method based on node features and structural information, which can efficiently generate node embeddings. We used 1500 graphs for training and 500 graphs for testing these baseline models and DBGNN. Table 1 presents the training time of four models. Figure 8 shows the loss and accuracy curves of these models during the training process. According to the data in Table 1, GraphSAGE has the shortest training time (1119.85 s), followed by GCN (1240.90 s). Our model requires 1452.77 s for training, which is slightly higher than GCN and GraphSAGE but significantly lower than GAT (5714.13 s). The extended training time of GAT is mainly due to the computational overhead introduced by its attention mechanism. Overall, our method strikes a balance between training cost and predictive accuracy. Figure 5: RPLAN floorplan data. Figure 6: The flow of bubble diagram extraction. Figure 8: The training curves of DBGNN and baseline models. \begin{table}
\begin{tabular}{c c} \hline \hline
**Model** & **Training Time** \\ \hline GCN & 1240.9033 s \\ GAT & 5714.1277 s \\ GraphSAGE & 1119.8463 s \\ DBGNN & 1452.7707 s \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Training time of DBGNN and baseline models. Figure 7: Data statistics of the bubble diagram dataset. As illustrated in Figure 8, GCN showed relatively steady performance, with a slow decrease in loss and noticeable fluctuations during training, resulting in unstable prediction performance, with a maximum accuracy of only 64%. This suggests that GCN struggles to handle the complex topological patterns in bubble diagrams. GAT showed some improvement over GCN, with reduced training fluctuations and a slight improvement in the rate of loss decrease, achieving a maximum accuracy of 75%. However, this indicates that GAT struggles to learn the implicit knowledge contained in the bubble diagram. GraphSAGE rapidly converged in the early stages of training, reaching a low loss and steadily improving prediction accuracy, demonstrating an advantage in both prediction tasks, suggesting that GraphSAGE is capable of learning different topological knowledge correctly. Among them, DBGNN performed the best, with rapid and smooth loss convergence and a quick improvement in prediction accuracy, reaching a maximum of 93%, demonstrating DBGNN's exceptional ability in handling both link prediction tasks. The test results are shown in Table 2. GCN achieves low prediction accuracy in wall and door link prediction tasks, with 65.93% ACC-Wall and 45.63% AP-Door. It can be argued that GCN fails to effectively learn the local and global patterns of bubble diagrams. GCN can encode structural information, but its low-pass filtering characteristics cause feature signals to converge, limiting its ability to learn bubble diagram patterns, resulting in poor link prediction accuracy. Similar to GCN, GAT performs poorly regarding door link prediction, achieving only 49.52% AP-Door. GAT improves the contribution of neighboring nodes' features by incorporating self-attention; however, it suffers from over-smoothing, which affects prediction accuracy. GraphSAGE performs better than GCN and GAT, with 86.63% ACC-Door and 76.24% ACC-Wall. GraphSAGE generates node embeddings by sampling and aggregating neighboring nodes' features, making it advantageous for handling large graph features, yet it is less suited for small bubble diagrams.