Quaternion Knowledge Graph Embeddings
Table 7: Analysis on different variants of scoring function. Same hyperparameters settings as QuatE3 are used.
['Analysis', '[BOLD] WN18 MRR', '[BOLD] WN18 Hit@10', '[BOLD] FB15K MRR', '[BOLD] FB15K Hit@10', '[BOLD] WN18RR MRR', '[BOLD] WN18RR Hit@10', '[BOLD] FB15K-237 MRR', '[BOLD] FB15K-237 Hit@10']
Ablation Study on Quaternion Normalization. We remove the normalization step in QuatE and use the original relation quaternion Wr to project head entity. This is likely because scaling effects in nonunit quaternions are detrimental. Hamilton Products between Head and Tail Entities. We reformulate the scoring function of QuatE following the original formulate of ComplEx. We do Hamilton product between head and tail quaternions and consider the relation quaternion as weight. Thus, we have ϕ(h,r,t)=Wr⋅(Qh⊗Qt). Additional Rotational Quaternion for Tail Entity. We hypothesize that adding an additional relation quaternion to tail entity might bring the model more representation capability. So we revise the scoring function to (Qh⊗W ◃ r)⋅(Qt⊗V◃r), where Vr represents the rotational quaternion for tail entity. However, it might cause some losses of efficiency.