# Translation-Based Embeddings with Octonion for Knowledge Graph Completion
## 4 Experiments and Discussion
### Experimental Results
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{6}{c}{**WN18 RR**} & \multicolumn{6}{c}{**FB15k-237**} \\ \cline{2-10}  & **MR** & **MRR** & **Hits@10** & **Hits@3** & **Hits@1** & **MR** & **MRR** & **Hits@10** & **Hits@3** & **Hits@1** \\ \hline TransE ([PERSON] et al., 2013) [9] & 3384 & 0.226 & 0.501 & - & - & 357 & 0.294 & 0.465 & - & - \\ DistMult ([PERSON] et al., 2014) [27] & 5110 & 0.430 & 0.490 & 0.440 & 0.390 & 254 & 0.241 & 0.419 & 0.263 & 0.155 \\ TuckER ([PERSON] et al., 2019) [29] & - & 0.470 & 0.526 & 0.482 & 0.443 & - & **0.358** & 0.544 & **0.394** & **0.266** \\ ComplEx-N3 ([PERSON] et al., 2018) [45] & - & 0.480 & 0.572 & 0.495 & 0.435 & - & 0.357 & 0.547 & 0.392 & 0.264 \\ RotatE ([PERSON] et al., 2019) [31] & 3340 & 0.476 & 0.571 & 0.492 & 0.428 & 177 & 0.338 & 0.533 & 0.375 & 0.241 \\ QuatE ([PERSON] et al., 2019) [32] & 2314 & 0.488 & 0.582 & 0.508 & 0.438 & 87 & 0.348 & **0.550** & 0.382 & 0.248 \\ ConvE ([PERSON] et al., 2018) [11] & 4187 & 0.430 & 0.520 & 0.440 & 0.400 & 244 & 0.325 & 0.501 & 0.356 & 0.237 \\ MuRE ([PERSON] et al., 2019) [19] & **2108** & 0.475 & 0.554 & 0.487 & 0.436 & 171 & 0.336 & 0.521 & 0.370 & 0.245 \\ AttE ([PERSON] et al., 2020) [20] & - & 0.490 & 0.581 & 0.508 & 0.443 & - & 0.351 & 0.543 & 0.386 & 0.255 \\ MuRP ([PERSON] et al., 2019) [19] & 2306 & 0.481 & 0.566 & 0.495 & 0.440 & 172 & 0.335 & 0.518 & 0.367 & 0.243 \\ AttH ([PERSON] et al., 2020) [20] & - & 0.486 & 0.573 & 0.499 & 0.443 & - & 0.348 & 0.540 & 0.384 & 0.252 \\ \hline TransO & 2269 & 0.499 & 0.599 & 0.519 & 0.445 & 169 & 0.347 & 0.534 & 0.383 & 0.253 \\ PTransO & 2416 & **0.504** & **0.602** & **0.524** & **0.455** & 169 & 0.345 & 0.531 & 0.381 & 0.251 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Link prediction results in high-dimensional space on WN18 RR and FB15k-237 datasets. while TransO performs only next to PTransO, ranking second on this dataset. The PTransO model's Hits@10 and MRR reached 0.602 and 0.504, which increased by 3.44% and 2.86%, respectively, compared with the previous best QuatE and AtE baseline models. Meanwhile, the TransO model's Hits@10 and MRR reached 0.599 and 0.499, which increased by 2.92% and 1.84%, respectively, compared with the previous best baseline models. Although the TransO and PTransO models did not achieve the best MR indicator, their MRs were also at a relatively advanced level compared to the baseline models. These results on the WN18 RR dataset reflect that: (1) it is effective to introduce the mathematical theories of octonion into the translation-based KGC method, since the comparison of TransO and advanced baseline models (including semantics-based and neural network-based, etc.) shows that TransO is generally at a satisfactory level; (2) in the environment of a hierarchical dataset, it is effective to introduce hyperbolic Poincare geometry into the translation-based KGC model, because, compared with TransO, PTransO shows an improvement in most indicators (except MR) and achieves state-of-the-art performance; the most obvious is that Hits@1 has increased by 2.25%. PTransO is only lower than TransO on the MR indicator. For this case, we consider that there are more false-positive samples in the test results of PTransO, i.e., the negative triples are wrongly judged as positive triples. Since the MR indicator is more vulnerable to false-positive samples [46], PTransO performs worse on MR than TransO. However, overall, PTransO has achieved a substantial improvement compared with TransO. In addition, by comparing the performance of the TransO model on the WN18 and WN18 RR datasets, respectively, in Tables 2 and 3, it can be seen that all indicators of the model on WN18 RR decreased significantly. This is mainly because WN18 RR removed the inverse and redundant triples from the WN18 dataset, and resolved the problem of data leakage that exists in WN18, where test triples can be trained directly through the inverse triples in the training and validation sets.