# Multi-Modal Entity Alignment Method Based on Feature Enhancement
## 3 Experiment and Discussion
### Optimization Objective  
We adopted the Intra-modal Contrastive Loss (ICL) and Inter-modal Alignment Loss (IAL) methods proposed by the MCLEA to train [10] and enable the model to fully capture the dynamics within and between modalities while maintaining semantic proximity and minimizing modal differences [22]. The ICL and IAL are formulated as follows:  
\[\delta_{m}(u,v)=\exp\Bigl{(}f_{m}(u)^{\top}f_{m}(v)/\tau\Bigr{)} \tag{12}\]  
\[q_{m}\Bigl{(}e_{1}^{i},e_{2}^{i}\Bigr{)}=\frac{\delta_{m}\Bigl{(}e_{1}^{i},e_{ 2}^{i}\Bigr{)}}{\delta_{m}\bigl{(}e_{1}^{i},e_{2}^{i}\Bigr{)}+\sum_{e_{1}^{i} \in N_{1}^{i}}\delta_{m}\Bigl{(}e_{1}^{i},e_{1}^{i}\Bigr{)}+\sum_{e_{2}^{i}\in N _{2}^{i}}\delta_{m}\Bigl{(}e_{1}^{i},e_{2}^{i}\Bigr{)}} \tag{13}\]  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Datasets** & **Language** & **Entities** & **Relations** & **Triplets** & **Image** & **Ref.** \\ \hline DBP15K\({}_{\text{ZH-EN}}\) & Chinese & 19,388 & 9812 & 318,449 & 15,912 & 15,000 \\  & English & 19,572 & 8496 & 438,360 & 14,125 & 15,000 \\ \hline DBP15K\({}_{\text{JA-EN}}\) & Japanese & 19,814 & 7181 & 326,205 & 12,739 & 15,000 \\  & English & 19,780 & 7219 & 414,100 & 13,741 & 15,000 \\ \hline DBP15K\({}_{\text{FR-EN}}\) & French & 19,661 & 5450 & 379,823 & 14,174 & 15,000 \\  & English & 19,993 & 7630 & 466,816 & 13,858 & 15,000 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The statistics of DBP15K.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Datasets** & **KG** & **Entities** & **Relations** & **Triplets** & **Image** & **Ref.** \\ \hline FB15K-DB15K & FB15K & 14,951 & 1461 & 621,608 & 13,444 & 12,846 \\  & DB15K & 12,842 & 504 & 137,277 & 12,837 & 12,846 \\ \hline FB15K-YAGO15K & FB15K & 14,951 & 1461 & 621,608 & 13,444 & 11,199 \\  & YAGO15K & 15,404 & 39 & 146,418 & 11,194 & 11,199 \\ \hline \hline \end{tabular}
\end{table}
Table 3: The statistics of FB15K-DB15K/YAGO15K.  
\[\mathcal{L}_{m}^{\text{ICL}}=-\mathbb{E}_{i\in\mathcal{B}}\log\left[\frac{1}{2} \left(q_{m}\left(e_{1}^{i},e_{2}^{i}\right)+q_{m}\left(e_{2}^{j},e_{1}^{i} \right)\right)\right] \tag{14}\]  
\[\mathcal{L}_{m}^{\text{IAL}}=\mathbb{E}_{i\in\mathcal{B}}\quad\frac{1}{2} \left[\text{KL}\left(q_{o}^{{}^{\prime}}\left(e_{1}^{i},e_{2}^{i}\right)\ \parallel q_{m}^{{}^{\prime}}\left(e_{1}^{i},e_{2}^{i}\right)\right)+\text{KL} \left(q_{o}^{{}^{\prime}}\left(e_{2}^{i},e_{1}^{i}\right)\ \parallel q_{m}^{{}^{\prime}}\left(e_{2}^{i},e_{1}^{i}\right)\right)\right] \tag{15}\]  
where \(\mathcal{L}_{m}^{\text{IAL}}\) and \(\mathcal{L}_{m}^{\text{IAL}}\) are the mean Intra-modal Contrastive Loss (ICL) and Inter-modal Alignment Loss (IAL); \(q_{m}\left(e_{1}^{i},e_{2}^{i}\right)\) is the probability distribution of the modality of \(m\) for positive pair \(\left(e_{1}^{i},e_{2}^{i}\right)\).  
\(\delta_{m}\left(e_{1}^{i},e_{2}^{i}\right)\) is the correlation probability between entities; it is calculated as shown in Equation (12), where \(f_{m}(.)\) is the encoder of the modality \(m\), and \(\tau\) is the hyperparameter. Additionally, \(q_{o}^{{}^{\prime}}\left(e_{1}^{i},e_{2}^{i}\right)\) and \(q_{o}^{{}^{\prime}}\left(e_{2}^{i},e_{1}^{i}\right)\) and \(q_{m}^{{}^{\prime}}\left(e_{1}^{i},e_{2}^{i}\right)\) and \(q_{m}^{{}^{\prime}}\left(e_{2}^{i},e_{1}^{i}\right)\) represent the output predictions with two directions of joint embedding and the uni-modal embedding of modality \(m\). KL refers to the KL divergence. When calculating the ICL and IAL, \(\tau\) is set to 0.1 and 4.0, respectively.