## 5 Conclusions  
This paper has proposed a simple and effective optimization framework for translation-based knowledge-graph embedding, which is named Op-trans. Op-Trans consists of two components: negative sampling by a cluster-cache sampling and weighting strategy, based on triplet-mapping properties. We address the inability of the knowledge-graph embedding model to obtain high-quality negative triplets, and propose cluster-cache sampling as a new negative sampling method. It largely improves the similarity between the replacement entity and the replaced entity, thereby improving the quality of the negative triplet. Furthermore, we assign a different mapping-weighting strategy to each triplet and provide positive feedback to the triplet that contributes more to the model training goal. It not only represents the hierarchical characteristics but is also flexible enough to adapt to the various mapping properties of the knowledge triplets. The experimental results also indicate that our method has a positive impact on completion ability compared with most baseline models. The biggest feature of our proposed Op-Trans method is its strong flexibility, which can effectively improve various basic models. However, our negative sampling approach incurs some maintenance costs due to the cache-update operation. In future work, we will discuss in detail the construction costs of our method in terms of time and storage space. We would like to extend our model to address knowledge-graph embedding in real-world applications with a smaller cost.  
Conceptualization, H.H.; methodology, H.H.; software, H.H.; validation, K.W. and X.L.; formal analysis, H.H.; investigation, H.H. and X.L.; resources, K.W.; data curation, H.H.; writing\(-\)original draft preparation, H.H.; writing\(-\)review and editing, H.H., X.L. and K.W.; visualization, H.H.; supervision, K.W.; project administration, K.W.; funding acquisition, K.W. All authors have read and agreed to the published version of the manuscript.  
This research was funded by Shanghai Science and Technology Innovation Action Planning (grant number:20 dz1203800).  
Not applicable.  
This research was supported by Shanghai Ocean University.  
The authors declare no conflict of interest.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Predicting Head (Hits@10)**} & \multicolumn{4}{c}{**Predicting Tail (Hits@10)**} \\ \cline{2-9}  & **1-to-1** & **1-to-N** & **N-to-1** & **N-to-N** & **1-to-1** & **1-to-N** & **N-to-1** & **N-to-N** \\ \hline TransE & 0.437 & 0.657 & 0.182 & 0.472 & 0.437 & 0.197 & 0.667 & 0.500 \\ Op-TransE & 0.503 & 0.776 & 0.231 & 0.523 & 0.514 & 0.232 & 0.747 & 0.685 \\ \hline TransH & 0.668 & 0.876 & 0.287 & 0.645 & 0.655 & 0.398 & 0.833 & 0.672 \\ Op-TransH & 0.759 & 0.893 & 0.315 & 0.741 & 0.759 & 0.400 & 0.841 & 0.717 \\ \hline TransR & 0.788 & 0.892 & 0.341 & 0.692 & 0.792 & 0.374 & 0.904 & 0.721 \\ Op-TransR & 0.796 & 0.927 & 0.339 & 0.765 & 0.793 & 0.378 & 0.925 & 0.817 \\ \hline TransD & 0.861 & 0.955 & 0.398 & 0.785 & 0.854 & 0.506 & 0.944 & 0.812 \\ Op-TransD & 0.874 & 0.962 & 0.441 & 0.822 & 0.881 & 0.566 & 0.958 & 0.854 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Detailed results on FB15K in terms of different relation categories.