HyperKG: Hyperbolic Knowledge Graph Embeddings for Knowledge Base Completion
Table 2: Experimental results on WN18RR and FB15k-237 test sets. MRR and H@10 denote the mean reciprocal rank and Hits@10 (in %), respectively. [⋆]: Results are taken from N18-2053 N18-2053.
['[BOLD] Method', '[BOLD] Type', '[BOLD] WN18RR MRR', '[BOLD] WN18RR H@10', '[BOLD] FB15k-237 MRR', '[BOLD] FB15k-237 H@10']
We give the results of our algorithm under the HyperKG listing. In the experiment where the Möbius addition was used, we removed the constraint for the entity vectors to have a norm less than 0.5. Although the Möbius addition is non-commutative, we found beneficial to keep the permutation matrix. Nonetheless, we do not use our regularisation scheme. Finally, the implausibility score is dp(s+′Πβo,r). Comparing the performance of the HyperKG variation using the Möbius addition against the performance of the HyperKG without regularisation, we can observe that we can achieve better results by using the Euclidean addition. This can be explained as follows. Instead, by using the Euclidean addition and since the hyperbolic metric is locally Euclidean, HyperKG can model facts for which the Euclidean Space is more appropriate by learning to retain small distances. Additionally, WN18RR contains more hierarchical relations compared to FB15k-237 Last but not least, we can observe that our proposed regularisation scheme is beneficial in terms of both MRR and Hits@10 on both datasets.