# Translation-Based Embeddings with Octonion for Knowledge Graph Completion
## 4 Experiments and Discussion
### Results in Modeling Different Types of Relations  
To test the representation capability of our models in modeling different types of relations, we design an ablation experiment in this section. In this experiment, we attempt to summarize the MRR for each relation on the WN18 RR dataset, and give the results shown in Table 5. The comparison models we selected are RotatE [31] and QuatE [32], which are typical KGC models that apply the mathematical theories of complex numbers and quaternions, respectively.  
According to Table 5, among the 11 relations, nine (81.82%) MRRs of TransO exceed or equal RotatE, and seven (63.64%) MRRs exceed or equal QuatE. These results indicate that, firstly, octonions have the representation capability to surpass complex numbers and quater  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**WN18 RR**} & \multicolumn{4}{c}{**FB15k-237**} \\ \cline{2-9}
**Model** & \multicolumn{3}{c}{**Hits**} & \multicolumn{3}{c}{**Hits**} \\ \cline{3-9}  & & **@10** & **@3** & **@1** & & **@10** & **@3** & **@1** \\ \hline TransE ([PERSON] et al., 2013) [9] & 0.182 & 0.419 & 0.266 & 0.053 & 0.147 & 0.259 & 0.158 & 0.089 \\ DistMult ([PERSON] et al., 2014) [27] & 0.327 & 0.379 & 0.351 & 0.293 & 0.178 & 0.332 & 0.197 & 0.100 \\ ComplEx-N3 ([PERSON] et al., 2018) [45] & 0.420 & 0.460 & 0.420 & 0.390 & 0.294 & 0.463 & 0.322 & 0.211 \\ RotatE ([PERSON] et al., 2019) [31] & 0.387 & 0.491 & 0.417 & 0.330 & 0.290 & 0.458 & 0.316 & 0.208 \\ ConvE ([PERSON] et al., 2018) [11] & 0.395 & 0.476 & 0.420 & 0.350 & 0.307 & 0.476 & 0.335 & 0.222 \\ MuRE ([PERSON] et al., 2019) [19] & 0.458 & 0.525 & 0.471 & 0.421 & 0.313 & 0.489 & 0.340 & 0.226 \\ RotE ([PERSON] et al., 2020) [20] & 0.463 & 0.529 & 0.477 & 0.426 & 0.307 & 0.482 & 0.337 & 0.220 \\ AttE ([PERSON] et al., 2020) [20] & 0.456 & 0.526 & 0.471 & 0.419 & 0.311 & 0.488 & 0.339 & 0.223 \\ MuRP ([PERSON] et al., 2019) [19] & 0.465 & 0.544 & 0.484 & 0.420 & 0.323 & 0.501 & 0.353 & 0.235 \\ RotH ([PERSON] et al., 2020) [20] & 0.472 & 0.553 & 0.490 & 0.428 & 0.314 & 0.497 & 0.346 & 0.223 \\ AttH ([PERSON] et al., 2020) [20] & 0.466 & 0.551 & 0.484 & 0.419 & 0.324 & 0.501 & 0.354 & **0.236** \\ \hline TransO & 0.471 & 0.558 & 0.493 & 0.421 & 0.324 & 0.501 & 0.356 & 0.235 \\ PTransO & **0.479** & **0.570** & **0.500** & **0.430** & **0.325** & **0.503** & **0.357** & 0.235 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Link prediction results in low-dimensional space on WN18 RR and FB15k-237 datasets.  
nions when modeling different types of relations; secondly, the combination of octonion and translation-based thoughts can compensate for the disadvantages of translation-based methods due to the shallow captured features to a certain extent, and generally achieves a performance gain over semantics-based methods on the WN18 RR dataset. In addition, compared with TransO, PTransO has MRRs greater than or equal to TransO on 7 of 11 (63.64%) relations, confirming the effectiveness of introducing hyperbolic geometry to improve hierarchical data representation.