## 5 Experiments
### Model Validation
In contrast, the original TransD fluctuates between 240 and 290 over the same range and only slightly outperforms the enhanced model at the lowest dimensions (50 and 100). Beyond 150 dimensions, Enhanced TransD rapidly surpasses the baseline and sustains its lead; above 200 dimensions, MR reductions plateau, indicating convergence toward optimal performance. Compared with TransE, TransH, and TransR, Enhanced TransD attains lower average MR in medium-to-high dimensions (\(\geq\)150), reducing MR by approximately 15-20% in the 250-300 range, which underscores the efficacy of attribute projection in augmenting entity feature representation in high-dimensional spaces. Regarding Mean Reciprocal Rank (MRR), Enhanced TransD exhibits a steady increase from \(\sim\)0.18 to \(\sim\)0.28 as dimensions grow from 50 to 300. By contrast, the original TransD only rises marginally from \(\sim\)0.19 to \(\sim\)0.20, with noticeable oscillations. Enhanced TransD's advantage emerges as early as 100 dimensions and maintains a 0.03-0.05 gain thereafter. TransE, TransH, and TransR show early MRR improvements but often suffer declines or stagnation above 200 dimensions, suggesting overfitting or optimization instability. The dual-limit loss effectively balances positive and negative gradient updates, securing consistent ranking accuracy across all dimensions. In terms of Hits@k metrics, Enhanced TransD outperforms baselines markedly: Hits@10 increases from \(\sim\)0.30 to \(\sim\)0.44 versus 0.37\(\sim\)0.36 for the original TransD; Hits@3 and Hits@1 rise from 0.20 to 0.32 and 0.10\(\sim\)0.20, respectively, achieving average gains exceeding 0.10. Relative to TransE, TransH, and TransR, the enhanced model's Hits@k improvements exceed 0.05 for all k values, with Hits@1--the strictest measure--demonstrating robust first-rank retrieval. Explicit encoding of domain attributes enables the model to more rapidly distinguish correct entity pairs amid a complex semantic space, thereby significantly boosting hit rates. Finally, classification metrics (Accuracy and F1 score) also improve notably. Accuracy climbs from \(\sim\)0.30 to \(\sim\)0.46 and F1 from \(\sim\)0.26 to \(\sim\)0.42 as dimensions increase, plateauing beyond 250 dimensions. This trend indicates that the dual-limit loss not only enhances ranking performance but also strengthens binary classification capability. However, marginal gains diminish at very high dimensions, suggesting that further increases in classification precision may require finer regularization, sparsity constraints, or multi-task learning strategies. Overall, experiments on FB15K-237 affirm the synergistic benefits of attribute projection and dual-limit loss, offering a novel optimization paradigm for translation-based knowledge graph embedding. As illustrated in Figure 10 for the WN18 RR dataset, experimental results on the WN18 RR dataset further demonstrate the applicability and robustness of Enhanced TransD for large-scale relational inference tasks. WN18 RR comprises nearly 40,000 entities and 11 relation types; compared with FB15K-237, it exhibits fewer relations but greater entity volume and path diversity, requiring models to capture long-range dependencies and multi-hop reasoning. Through the synergistic effects of attribute projection vectors and the dual-limit loss, Enhanced TransD significantly outperforms baseline models (TransE, TransH, TransR, and original TransD) across MR, MRR, and Hits@k metrics, confirming its adaptability to diverse knowledge graph structures. Figure 9: Performance of translation-based knowledge graph embedding models on the FB15K-237 dataset across varying embedding dimensions. In terms of mean rank (MR), Enhanced TransD reduces MR from approximately 3726 at 50 dimensions to 2766 at 300 dimensions--a decline exceeding 25%. By contrast, the original TransD only lowers MR from about 4463 to 3532 over the same range.