# Translation-Based Embeddings with Octonion for Knowledge Graph Completion
## 4 Experiments and Discussion
### Experimental Results  
Table 2 shows the link prediction results of TransO on the WN18 dataset; Tables 3 and 4 show the link prediction results of TransO and PTransO on the WN18 RR and FB15k-237 datasets, respectively, in high-dimensional and low-dimensional embedded spaces. In Tables 2-4, the best results are marked in bold, and the second-best results are underlined. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Dataset** & **Entites** & **Relations** & **Triples** & **\#Training** & **\#Validation** & **\#Test** \\ \hline WN18 & 40,943 & 18 & 151k & 141,442 & 5000 & 5000 \\ WN18 RR & 40,943 & 11 & 93k & 86,835 & 3034 & 3134 \\ FB15k-237 & 14,951 & 237 & 310k & 272,115 & 17,535 & 20,466 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Dataset statistics. According to the experimental results in Table 2, TransO performs well on the WN18 dataset, and achieves state-of-the-art performance compared with the baseline models. The Hits@10 of TransO reached 0.962, increased by 1.26% compared with the previous best TransAT model; Hits@3 reached 0.942, increased by 2.06% compared with the previous best TransD model. However, for the Hits@1 indicator, TransO achieved a surprising improvement compared with the translation models, and nearly doubled the previous best TransR model. We analyze that the reason for this experimental result is that we introduced the octonion feature interaction, which causes the translation-based TransO to have the capabilities to mine the deep interaction features similarly to the semantic models, thereby improving the predictive effects on Hits@1. To validate this view, we added a comparison with the semantics-based DistMult model. It can be seen that DistMult also has been greatly improved compared with the translation baseline models on the Hits@1 indicator, which is consistent with the TransO model. Compared with DistMult, TransO performed better in all indicators, which reflects that the translation model can also have similar or stronger expressive capabilities compared to the semantic models by combining the method of octonion feature interaction. Moreover, the results on the MR and MRR indicators also indicate that TransO can improve the ranking of correct entities in the list of candidate entities in the process of link prediction, and it can more easily find the correct results from the list of candidate entities than other baseline models. The above experimental results preliminarily verify the feasibility of introducing the mathematical methods of octonion into the translation-based KGC model. It can be seen from the experimental results in Table 3 that the PTransO and TransO models perform well on the WN18 RR dataset in high-dimensional embedded space, in which most indicators (except MR) of PTransO achieve state-of-the-art performance, \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Model** & **MR** & **MRR** & **Hits@10** & **Hits@3** & **Hits@1** \\ \hline TransE ([PERSON] et al., 2013) [9] & 251 & 0.454 & 0.934 & 0.823 & 0.089 \\ TransFI ([PERSON] et al., 2014) [21] & 388 & 0.485 & 0.936 & 0.916 & 0.060 \\ TransR ([PERSON] et al., 2015) [22] & 225 & 0.605 & 0.940 & 0.876 & 0.335 \\ TransD ([PERSON] et al., 2015) [23] & 212 & 0.580 & 0.942 & 0.923 & 0.241 \\ STransE ([PERSON] et al., 2016) [24] & 206 & 0.657 & 0.934 & - & - \\ TransSparse ([PERSON] et al., 2016) [25] & 211 & - & 0.932 & - & - \\ TransAT ([PERSON] et al., 2018) [26] & 157 & - & 0.950 & - & - \\ DistMult ([PERSON] et al., 2014) [27] & 902 & 0.822 & 0.934 & 0.914 & 0.728 \\ \hline TransO & **98** & **0.918** & **0.962** & **0.942** & **0.889** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Link prediction results of TransO on WN18 dataset.