## 3 Proposed Method
### Review of Translation Model Framework  
Translation models interpret relations as geometric transformations in the latent space. They consider the relation \(r\) in the triplet \((h,r,t)\) as a translation from the head entity \(h\) to the tail entity \(t\). In this way, when two facts (China, Capital, Beijing) and (UK, Capital, \begin{table}
\begin{tabular}{c c} \hline \hline
**Symbols** & **Concepts** \\ \hline \(E\) & The entity set of the knowledge graph \\ \(R\) & The relation set of the knowledge graph \\ \(h,r,t\) & Head entity, relation, and tail entity, \\  & respectively. \(h,t\in E\), \(r\in R\) \\ \(h\),\(r\),\(t\) & The embedding vector of \(h,r,t\) \\ \(\Delta\) & The triplet set of the knowledge graph \\ \((h,r,t)\) & The triplet in the knowledge graph, \\  & \((h,r,t)\in\Delta\) \\ \(\Delta^{\prime}\) & The negative triplet set generated \\ \((h^{\prime},r,t^{\prime})\) & The negative triplet that is not in the knowledge graph, \((h^{\prime},r,t^{\prime})\in\Delta^{\prime}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The general concepts and symbols in this paper. London) have the same semantic relation, the word vectors exist in the embedding space: China-Beijing \(\approx\) UK-London. Translation models have a common principle that _h+r\(\approx\)t_. We used the most typical TransE model as an analysis case. Figure 3 shows the triplet structure of the TransE. In translation models, the scoring function can model the complex interactions between entities and relations. For a given positive triplet, the distance between _h+r_ and \(t\) is expected to be reduced in the corresponding space, i.e., the sum of the head entity vector \(h\) and the relation vector \(r\) should be approximately the same as the tail entity vector \(t\). Conversely, for a negative triplet, the distance between _h+r_ and \(t\) is expected to be far away from the corresponding space. The translation model uses the distance between _h+r_ and \(t\) in the embedding space to measure the probability that the triplet is incorrect, and it defines the scoring function as shown in Equation (1). \[f(h,r,t)=\left\|\textbf{{h+r-t}}\right\|_{1/2} \tag{1}\]  
\(f(h,r,t)\) can be considered as the deviation degree of the vector _h+r_ from \(t\) after the triplet embedding. Therefore, the smaller the value of the scoring function, the more likely the triplet is to be correct. It requires lower scores for positive triplets and higher scores for negative triplets. During the training process, the set of training triplets will be randomly traversed multiple times, and a batch \(\Delta batch\) of size \(b\) will be extracted from the training triplet set at each iteration. Whenever we access a positive triplet and need to generate a negative triplet, the TransE model randomly selects an entity from the entity set to generate a negative triplet, which is not contained in the set of \(\Delta\). The set of negative triplets is shown in Equation (2). \[\Delta^{\prime}_{(h^{\prime},r,t^{\prime})}=\left\{(h^{\prime},r,t)\
otin \Delta\big{|}h^{\prime}\in E\right\}\cup\left\{(h,r,t^{\prime})\
otin\Delta \big{|}t^{\prime}\in E\right\} \tag{2}\]  
With the factual information, the embeddings are learned by solving the optimization problem that minimizes the scoring function for positive triplets and maximizes it for negative triplets at the same time. Then, we define the following margin-based loss as the training goal:  
\[\updownarrow=\sum_{(h,r,t)\in\Delta,(h^{\prime},r,t^{\prime})\in\Delta^{ \prime}}\left[f(h,r,t)-f(h^{\prime},r,t^{\prime})+\gamma\right]_{+} \tag{3}\]  
where \(\gamma\) is the margin hyper-parameter separating the positive and negative triplets, \(\left[x\right]_{+}=\max(0,x)\). The embedding parameters are then updated after each iteration of the model. Although translation models have made greater progress in the link prediction task, researchers have made many contributions to enable a better vector representation of entities and relations.