## 5 Experiments  
### Model Validation  
(1) Datasets  
This study selects FB15K-237 and WN18 RR as benchmark datasets for evaluation, effectively mitigating the inverse-relation leakage issues present in their predecessor datasets and thus ensuring the rigor and reliability of the evaluation results. FB15K-237 and WN18 RR are derived from FB15K and WN18, respectively, by removing redundant inverse relations, thereby reducing performance inflation in the test sets caused by duplicated information. This combined dataset configuration not only reflects the model's capability to generalize across sparse and de-noised knowledge graphs but also demonstrates its potential for application in high-complexity domains. Detailed statistics of these datasets are provided in Table 3.  
(2) Experimental Design  
In the data preprocessing stage, we uniformly extract all original triples and each entity's intrinsic attributes, constructing separate mapping dictionaries for entities, relations, and attributes to convert textual information into corresponding integer indices. A full-set triple filter is also generated to automatically mask known positive samples during subsequent training and validation. In this stage, we standardize all field formats and impute or discard missing values in critical attributes according to domain-specific rules. We then normalize date/time fields to a uniform format and clean categorical strings by trimming whitespace, applying consistent casing, and removing special characters. Subsequently, each unique entity name, relation label, and attribute value is mapped to a corresponding integer index via dedicated lookup tables. Numerical attributes are scaled to facilitate convergence during training, and referential integrity is verified across the head-relation-tail triples. Finally, the fully cleaned and indexed triple set is randomly partitioned into training, validation, and test subsets using a fixed seed. Additionally, a full-set filter is applied to mask known positive triples during subsequent model fitting and evaluation. During model construction, dropout layers are incorporated into the entity embeddings, relation embeddings, and newly introduced attribute projection vectors, and independent \(L_{2}\) regularization is applied to each of these three vector types to mitigate overfitting while maintaining a balance between attribute and structural information. To address the skewed distribution of head and tail entities, negative samples are generated according to a Bernoulli sampling strategy that respects the relation-specific corruption ratios. We replace the single-margin loss with a dual-limit loss to achieve finer control over the score distributions of positive and negative samples. Training proceeds in mini-batches, with block-wise candidate entity search to ensure that, even under GPU memory constraints, scores and gradients for all entities within each batch are correctly computed and updated. To assess the effect of embedding dimensionality on the generalization and representational capacity of the enhanced TransD model, we conducted unified training \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Data Set** & **Number of** & **Number of** & **Size of** & **Size of** & **Size of** \\  & **Entities** & **Relationships** & **Training Set** & **Validation Set** & **Size of Test Set** \\ \hline FB15K-237 & 14,541 & 237 & 272,115 & 17,535 & 20,466 \\ WN18 RR & 40,943 & \(11\) & 86,835 & 3034 & 3134 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Statistics of the validation datasets for model evaluation. and evaluation at dimensions of 50, 100, 150, 200, 250, and 300. Comparative experiments against TransE, TransH, TransR, and the original TransD were performed to comprehensively validate the advantages of our enhancement.