# Dual Quaternion Embeddings for Link Prediction
## 6 Conclusions  
In this paper, we propose a novel model, DualQuatE, for knowledge graph embedding, which maps entities and relations to dual quaternion space. We present a new score function to model each relation as interaction of rotation and translation, which addresses the multiple relations between two entities. We demonstrate that our model is able to express main relation patterns and outperforms state-of-the-art baselines. However, DualQuatE does not consider temporal information and semantic hierarchies in knowledge graphs. In the feature, we will investigate how to explore temporal information and semantic hierarchies based on our model. It is also interesting to investigate the possibility of  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Method** & **Space Complexity** & **Time Complexity** \\ \hline TransE & \(\mathcal{O}(nd+md)\) & \(\mathcal{O}(d)\) \\ RotatE & \(\mathcal{O}(nd+md)\) & \(\mathcal{O}(d)\) \\ HAKE & \(\mathcal{O}(nd+md)\) & \(\mathcal{O}(d)\) \\ RESCAL & \(\mathcal{O}(nd+md^{2})\) & \(\mathcal{O}(d^{2})\) \\ HolE & \(\mathcal{O}(nd+md)\) & \(\mathcal{O}(dlogd)\) \\ ComplEx & \(\mathcal{O}(nd+md)\) & \(\mathcal{O}(d)\) \\ QuatE & \(\mathcal{O}(nd+md)\) & \(\mathcal{O}(d)\) \\ DualQuatE & \(\mathcal{O}(nd+md)\) & \(\mathcal{O}(d)\) \\ \hline \hline \end{tabular}
\end{table}
Table 6: Space and Time Complexity.  
Figure 4: Visualization of relation patterns represented by DualQuatE in rotation, where (**a**) denotes the symmetry relation “similar_to” in rotation of **mm**, (**b**,**c**) are rotations of “has_part” and “part_of”, and (**d**) exhibits the inversion effects, where “has_part” * “part_of” represents **mm**\({}^{\prime}\).  
applying our DualQuatE model to learning representations of propositions for helping learning action models [25; 26; 27; 28] and recognizing plans [29; 30; 31] in planning community.  
Conceptualization, L.G., H.Z. and H.H.Z.; methodology, L.G. and H.Z.; software, L.G.; validation, L.G., H.Z. and H.H.Z.; formal analysis, L.G. and H.H.Z.; investigation, L.G. and H.Z.; resources, L.G., H.Z. and H.H.Z.; data curation, L.G.; writing--original draft preparation, L.G.; writing--review and editing, H.Z. and H.H.Z.; visualization, L.G.; supervision, H.Z., H.H.Z. and J.X.; project administration, L.G.; funding acquisition, H.Z. and H.H.Z. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (Grant No. 62076263), the National Natural Science Foundation of China for Young Scientists of China (Grant No. 11701592), the Joint Funds of the National Natural Science Foundation of China (Grant No. U1811263), Guangdong Natural Science Funds for Distinguished Young Scholar (Grant No. 2017A030306028), Guangdong special branch plans young talent with scientific and technological innovation (Grant No. 2017 TQ04X866), Pearl River Science and Technology New Star of Guangzhou and Guangdong Province Key Laboratory of Big Data Analysis and Processing.  
Not applicable.  
**Data Availability Statement:** Publicly available datasets were analyzed in this study. These data can be found here: [[https://github.com/gaoliming123/DualQuatE](https://github.com/gaoliming123/DualQuatE)]([https://github.com/gaoliming123/DualQuatE](https://github.com/gaoliming123/DualQuatE)), accessed on 11 June 2021.  
The authors declare no conflict of interest.