# Dual Quaternion Embeddings for Link Prediction
## 5 Experiments
### Results  
Tables 3-5 show the experimental results on four datasets. The performance of DualQuatE and its variations represent comparability to state-of-the-art models. For YAGO3-10, the link prediction results are shown in Table 3, from which we can see that DualQuatE is competitive compared to most previous knowledge graph embedding models, especially in metric Hit@10. The result of YAGO3-10 tells us that the performance of DualQuatE is better than DualQuatE-1, which indicates that modeling relations as the interaction of rotation and translation with more degrees of freedom (as done by DualQuatE) is indeed better than simply modeling relations as rotation (as done by DualQuatE-1). Furthermore, the advanced results of DualQuatE-2 and DualQuatE inspire us to explore the mixed effects of vector operations. Tables 4 and 5 indicate the effects of our models on four common datasets: WN18 RR, FB15k-237, WN18 and FB15k. We can find that our models perform better on datasets WN18 RR and FB15k-237; for WN18 and FB15k, metrics are almost close to previous models and several metrics surpass the previous. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**F15k-237**} & \multicolumn{6}{c}{**WN18 RR**} \\ \hline
**Model** & **MR** & **MRR** & **Hit@1** & **Hit@3** & **Hit@10** & **MR** & **MRR** & **Hit@1** & **Hit@3** & **Hit@10** \\ \hline TransE \(\clubsuit\) & 357 & 0.294 & - & - & 0.465 & 3384 & 0.226 & - & - & 0.501 \\ ComplEx \(\clubsuit\) & 339 & 0.247 & 0.158 & 0.275 & 0.428 & 5261 & 0.44 & 0.41 & 0.46 & 0.51 \\ RotatE \(\clubsuit\) & 177 & 0.338 & 0.241 & 0.375 & 0.533 & 3340 & 0.476 & 0.428 & 0.492 & 0.571 \\ DihEdral & - & 0.32 & 0.23 & 0.353 & 0.502 & - & 0.48 & **0.452** & 0.491 & 0.536 \\ QuatE \(\clubsuit\) & 176 & 0.311 & 0.221 & 0.342 & 0.495 & 3472 & 0.481 & 0.436 & 0.500 & 0.564 \\ InteractE & 172 & **0.354** & **0.263** & - & 0.535 & 5202 & 0.463 & 0.430 & - & 0.528 \\ HAKE & - & 0.346 & 0.250 & 0.381 & 0.542 & - & **0.497** & **0.452** & **0.516** & **0.582** \\ \hline DualQuatE-1 & 173 & 0.329 & 0.230 & 0.368 & 0.530 & 2989 & 0.463 & 0.408 & 0.484 & 0.571 \\ DualQuatE-2 & 174 & 0.345 & 0.246 & **0.384** & **0.545** & 3324 & 0.484 & 0.437 & 0.503 & 0.576 \\ DualQuatE & **171** & 0.342 & 0.245 & 0.381 & 0.535 & **2755** & 0.470 & 0.415 & 0.493 & **0.582** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Link prediction on datasets FB15k-237 and WN18 RR. \(\clubsuit\) represents the results that came from ([PERSON] et al., 2019) and the others came from the original papers. \(\clubsuit\) denotes the results of QuatE without type constraints from the paper. The results with bold are the best and the underlined ones are the second best results. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{6}{c}{**YAGO3-10**} \\ \hline
**Model** & **MR** & **MRR** & **Hit@1** & **Hit@3** & **Hit@10** \\ \hline DistMult \(\clubsuit\) & 5926 & 0.34 & 0.24 & 0.38 & 0.54 \\ ComplEx \(\clubsuit\) & 6351 & 0.36 & 0.26 & 0.40 & 0.55 \\ ConvE \(\clubsuit\) & 1671 & 0.44 & 0.35 & 0.49 & 0.62 \\ RotatE & 1767 & 0.495 & 0.402 & 0.550 & 0.670 \\ InteractE & 2375 & 0.541 & **0.462** & - & 0.687 \\ HAKE & - & **0.545** & **0.462** & **0.596** & 0.694 \\ \hline DualQuatE-1 & 1636 & 0.477 & 0.377 & 0.534 & 0.672 \\ DualQuatE-2 & 1889 & 0.503 & 0.411 & 0.557 & 0.676 \\ DualQuatE & **1210** & 0.534 & 0.445 & 0.591 & **0.695** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Link prediction on datasets YAGO3-10. \(\clubsuit\) represents the results that came from ([PERSON] and [PERSON], 2015) and the others came from the original papers. The results with bold are the best and the underlined ones are the second best results.