# Translation-Based Embeddings with Octonion for Knowledge Graph Completion
## 4 Experiments and Discussion
### Experimental Results
Therefore, there is no longer an \"inversion\" relation pattern in the WN18 RR dataset, and the model can achieve significantly worse performance on this dataset than on the original WN18, but the evaluation on the WN18 RR dataset is more conducive to reflecting the true modeling capabilities. However, on the FB15k-237 dataset, there is still a certain gap between our methods and the state-of-the-art model in high-dimensional embedded space. The TransO model's Hits@10 and MRR reached 0.534 and 0.347, which increased by 14.83% and 18.02% compared with the TransE model, but are still 3.00% and 3.17% lower, respectively, than the QuatE and TuckER models, which performed best among the baseline models. PTransO's performance on FB15k-237 is close to TransO, and is slightly lower than TransO on most indicators. Moreover, the MR indicators of our models on this dataset are at a moderate level, and their performance is similar to that of the RotatE, MuRP, and MuRE models with geometric methods. Although significantly better than the translation-based TransE model, there is still a large gap compared with the semantics-based QuatE model. The TransO and PTransO models underperform on the FB15k-237 dataset embedded in high-dimensional vector space. We analyze that the main reason is that the translation-based models have insufficient modeling capabilities for the datasets with complex relational types. The FB15k-237 dataset is derived from Freebase and contains various types of common information, including human, social, and geographical information. There are 237 relations in the FB15k-237 dataset, compared with only 11 relations in WN18 RR. The translation-based models ultimately measure the distance between the head entities interacting with relations and the tail entities only through the \(l1\) or \(l2\)-norm, and generally have weaker capabilities to distinguish similar relations than semantic or neural network models. Although the bias parameters \(b_{had}\) and \(b_{tail}\) are added to the models that we propose, they are only entity-specific parameters and have nothing to do with the relations. TransO performs slightly better than PTransO on the FB15k-237 dataset embedded in high-dimensional space. We analyze that the main reason is that the FB15k-237 dataset is not hierarchical. Reviewing Section 3.1.2, we can see that hyperbolic geometry has inherent advantages in modeling capabilities compared with Euclidean geometry under the condition of hierarchical data or low-dimensional vector space, but if both conditions are not met, hyperbolic geometry has no obvious advantages over Euclidean geometry, i.e., the advantages of hyperbolic geometry cannot be utilized without low-dimensional space and hierarchical datasets. Moreover, the introduction of hyperbolic Poincare geometry into the TransO model requires the indirect construction of a Euclidean-like space using tangent space \(\mathcal{T}_{0}^{\mathrm{c}}\). Frequent use of the mapping from tangent space \(\mathcal{T}_{0}^{\mathrm{c}}\) to Poincare space \(\mathbb{B}^{d,c}\) may result in calculation errors that affect the accuracy of model predictions. By analyzing the deficiencies of our models in Table 3, if we can find a method to improve the modeling capability of the translation model for complex datasets with a large number of relations, or find a method that can directly use the octonion in the hyperbolic Poincare space rather than in the tangent space, we may further improve the performance. As can be seen from Table 4, the PTransO model achieves state-of-the-art performance on the WN18 RR dataset, and its Hits@10 and MRR reach 0.570 and 0.479, which have increased by 3.07% and 1.48%, respectively, compared with the previous best RotH baseline model. Moreover, PTransO basically achieves the best effect on FB15k-237 (except Hits@1), and its Hits@10 and MRR reached 0.503 and 0.325, which increased by 0.40% and 0.31%, respectively, compared with the previous best AttH baseline model.