## 5 Experiments
### Model Application
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Data Set** & **Number of Entities** & **Number of Relationships** & **Size of Training Set** & **Size of Validation Set** & **Size of Test Set** \\ \hline TAKG & 33,755 & 115 & 460,005 & 57,495 & 57,500 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Detailed statistics of the Traffic Accident Knowledge Graph (TAKG). The Mean Reciprocal Rank (MRR) reflects the model's effectiveness in ranking correct entities near the top of candidate lists. In the lower embedding range (50-150), due to indistinct margins between positive and negative samples, MRR remains between 0.528 and 0.530. As the dimension increases, the dual-limit loss independently enforces suitable margins for positive and negative samples, concentrating high-scoring positives toward the top. Consequently, MRR begins to rise after 200 dimensions and peaks at 0.552 at 250 dimensions--substantially above the low-dimensional stage. Although MRR slightly declines at 300 dimensions, it still exceeds its initial levels, indicating that the dual-limit loss maintains strong discriminative power in the expanded embedding space. Figure 13: Performance of the enhanced TransD model on the Traffic Accident Knowledge Graph (TAKG) across different embedding dimensions. Similarly, Hits@10, Hits@3, and Hits@1 show steady upward trends across dimensions: Hits@10 increases from 0.6135 to 0.6185 at 250 dimensions, Hits@3 rises from 0.5635 to 0.5830, and Hits@1 jumps from 0.4800 to 0.5105 at 250 dimensions. These gains primarily stem from the inclusion of attribute projection vectors, which draw true positives closer within the top candidate positions, and the dual-limit loss, which further separates positives from near-neighbor negatives--most prominently under the strict Hits@1 criterion. The slight declines observed at 300 dimensions further corroborate the general tendency toward overfitting and noise induction in excessively high-dimensional spaces. In the node-classification tasks assessed by Accuracy and F1-score, the model likewise attains optimal performance at 250 dimensions: Accuracy improves from 0.48 at 50 dimensions to 0.51 at 250 dimensions, and F1-score rises from 0.65 to 0.68; at 300 dimensions, both metrics decline to approximately 0.49 and 0.655, respectively. The gains in classification accuracy stem primarily from the dual-limit loss, which simultaneously elevates the scores of negative samples and suppresses those of positive samples, thereby establishing clearer decision boundaries in the mid-dimensional embedding space. The improved F1-score further indicates enhanced detection of minority classes, such as rare accident types. Similar performance trends observed on general benchmarks like FB15K-237 and WN18 RR suggest the broad applicability of this enhancement across diverse knowledge graphs. In our experiments, we augment the TransD dynamic mapping with attribute projection vectors and adopt a dual-limit scoring loss. Each attribute projection vector is dedicated to critical accident attributes--such as time, location, weather, and severity--enabling entity embeddings to encode multidimensional attribute information alongside relational mappings. This design allows the model to extract richer semantic features even at low to mid embedding dimensions, yielding superior performance on fine-grained ranking metrics like Hits@1. The dual-limit loss applies distinct margins to positive and negative samples: on one hand, it ensures positive samples cluster without over-compression; on the other, it enforces a robust separation between negatives and positives. Together, these mechanisms synergize in the mid to high embedding space, driving MR, MRR, Hits@K, and classification metrics to peak at 250 dimensions. Below this threshold, the embedding space is too constrained to balance attribute encoding with relation mapping; above it, excessive parameters induce overfitting and performance degradation.