# A Novel Embedding Model for Knowledge Graph Entity Alignment Based on Graph Neural Networks
## 4 Experiments
### Main Results and Analysis  
Tables 2 and 3 illustrate the cross-lingual performance of various models, all exhibiting bidirectional best alignment outcomes. The tables provide a breakdown of Hits@k in percentages, with the best results of the baseline denoted in bold, while the PCE-HGTRA model's superior performance is signified by underlined numbers. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Datasets** & **KGs** & **Entities** & **Relations** & **Rel.Triples** & **Pro.Triples** \\ \hline \multirow{2}{*}{EN-DE-15K-V1} & English & 15,000 & 215 & 47,676 & 83,755 \\  & German & 15,000 & 131 & 50,419 & 156,148 \\ \hline \multirow{2}{*}{EN-DE-15K-V2} & English & 15,000 & 169 & 84,867 & 81,988 \\  & German & 15,000 & 96 & 92,632 & 186,333 \\ \hline \multirow{2}{*}{EN-FR-15K-V1} & English & 15,000 & 267 & 47,334 & 73,121 \\  & French & 15,000 & 210 & 40,864 & 67,167 \\ \hline \multirow{2}{*}{EN-FR-15K-V2} & English & 15,000 & 193 & 96,318 & 52,355 \\  & French & 15,000 & 166 & 80,112 & 56,113 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Statistics of datasets. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Datasets** & \multicolumn{4}{c}{**EN-DE-15K-V1**} & \multicolumn{4}{c}{**EN-DE-15K-V2**} \\ \hline
**Model** & **Hits@1** & **Hits@5** & **Hits@10** & **MR** & **Hits@1** & **Hits@5** & **Hits@10** & **MR** \\ \hline MTransE & 11.85 & 24.15 & 30.42 & 586.78 & 1.9 & 5.39 & 7.96 & 1045.27 \\ JAPE & 12.82 & 26.86 & 34.13 & 342.67 & 2.57 & 6.92 & 10.04 & 847.1 \\ IPTransE & 50.23 & 68.32 & 76.2 & 183.01 & 60.74 & 76.43 & 82.02 & 23.93 \\ RDGCN & 43.38 & 55.31 & 59.47 & 828.38 & 58.57 & 69.83 & 73.35 & 560.06 \\ SEA & 53.45 & 72.31 & 80.05 & 125.25 & 60.55 & 78.14 & **84.23** & **16.07** \\ IMUSE & **61.01** & **75.38** & **80.33** & **76.75** & **63.03** & **78.32** & 82.82 & 19.71 \\ GCN-Align & 47.01 & 67.86 & 75.05 & 150.45 & 34.97 & 55.02 & 62.89 & 130.81 \\ PCE-HGTRA & 62.63 & 76.77 & 80.84 & 68.74 & 64.97 & 80.76 & 85.52 & 15.93 \\ Improv.best & 1.62 & 1.39 & 0.51 & 8.01 & 1.94 & 2.44 & 1.29 & 0.14 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results from the experiments conducted on EN-DE-15K-V1 and EN-DE-15K-V2 datasets. Results of OpenEA: According to the data in Tables 2 and 3, PCE-HGTRA performed the best on three out of four datasets and still had the best MR index on the fourth dataset. Additionally, it exceeded the best baseline by 1.62% to 7.94% on the Hits@1 indicator. IMUSE's performance on the OpenEA dataset was almost equivalent to that of PCE-HGTRA, effectively utilizing the properties and relationship information existing in the KG. However, PCE-HGTRA still achieved outstanding performance. The OpenEA model reduced the number of relationships and triplets, challenging the modeling ability of sparse KGs. The PCE-HGTRA achieved significant improvements over both dense and sparse KG baselines. Notably, the improvement achieved by our approach on the Hits@1 metric exceeded that on Hits@5, implying that PCE-HGTRA can more precisely identify true entities among the top five alignment candidates that are difficult to distinguish. The experiments showed that PCE-HGTRA can partially address the problem of neighborhood sparsity for certain entities. It is noteworthy that, despite not being able to precisely identify the top 10 alignment candidates on the EN_FR_15K_V2 dataset, our model still achieved an optimal MR index, highlighting the superior recall performance of our method compared to the baseline. As expected, GNN-based methods generally achieve good results, while entity alignment models based on TransE perform poorly in the EA task due to embeddings of different KGs residing in different vector spaces and a lack of proper conversion methods. MTransE represents entities across distinct vector spaces, albeit with a potential loss of information during the transformation learning process. IPTransE improves upon TransE by specifying corresponding conversion rules between entities through their paths.