# An Approach to Knowledge Base Completion
## 6 Experiments
### Experimental Results  
Table 5 shows the results of the proposed model for WN18 data set. 'Head' implies candidate triples are generated by swapping head entities. Thus, it is the problem of finding correct head entities. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Data Set** & **FB15K** & **WN18** \\ \hline \# of Entities & 14,951 & 40,943 \\ \# of Relations & 1345 & 18 \\ \# of Training Triples & 483,142 & 141,441 \\ \# of Validation Triples & 50,000 & 5000 \\ \# of Test Triples & 59,071 & 5000 \\ \# of Total Triples & 592,213 & 151,441 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Simple statistics on data sets. Similarly, 'Tail' is the problem of finding correct tail entities. As noted above, all values in this table are measured by Hits@_k_. Thus, 'Average' implies the average of Hits@_k_ of 'Head' and that of 'Tail'. Overall, the performance of all models gets worse as \(k\) gets smaller. That is, the values of Hits@10's are higher than those of Hits@3's and Hits@1's, and Hits@3's are higher than Hits@1's. This is natural because the smaller \(k\) gets, the less probable it is that a candidate triple becomes an actual fact. In addition, ComplEx always achieves the highest performance among the baseline models, and TransR achieves the lowest, on average. When \(k\) = 10, ComplEx achieves the highest Hits@10 of 0.8, while TransR does the lowest Hits@10 of 0.579. The Hits@3 of ComplEx is 0.647 which is nearly double of that of TransR. Specifically, it achieves 0.455 in Hits@1, and is around 10 times higher than that of TransE. The proposed model noted as 'committee-based model' outperforms all these baseline models. Its Hits@10 is 0.824, Hits@3 is 0.691, and Hits@1 is 0.495. The experimental results for FB15K data set are shown in Table 6. The performance for FB15K data set is lower than that for WN18 data set. This is because that the size of FB15K is larger than that of WN18 despite the smaller number of entities. The performances of TransE and TransR in Hits@10 are 0.467 and 0.377, respectively. Their Hits@3's are 0.228 and 0.187, while Hits@1's are 0.030 and 0.052. Although both DistMult and ComplEx achieve higher results for all Hits@10, Hits@3, and Hits@1, DistMult outperforms ComplEx for this data set. That is, DistMult is the best baseline model for this data set. However, the proposed committee-based model is superior to DistMult even in FB15K. Hits@10 of the proposed model is 0.532, its Hits@3 is 0.305, and its Hits@1 is 0.162. All these values are much higher than those of the baseline models regardless of \(k\). These experimental results prove the effectiveness of the proposed committee model. Since the proposed model can reflect various aspects of a knowledge graph by combining various knowledge graph embeddings, it outperforms the baseline models. Figure 2 proves this fact. This figure depicts how Hits@_k_ changes as \(k\) decreases from ten to one. Figure 2a shows the change of Hits@_k_ for WN18 data set, and Figure 2b is about FB15K data set. The performance of all models naturally decreases as \(k\) \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & **TransE** & **TransR** & **DistMult** & **ComplEx** & **Committee-Based Model** \\ \hline \multirow{4}{*}{**Tail**} & Head & 0.434 & 0.344 & 0.483 & 0.465 & 0.501 \\  & Tail & 0.501 & 0.410 & 0.551 & 0.526 & 0.564 \\  & Average & 0.467 & 0.377 & 0.517 & 0.495 & 0.532 \\ \hline \multirow{4}{*}{**Tail**} & Head & 0.213 & 0.167 & 0.272 & 0.260 & 0.281 \\  & Tail & 0.244 & 0.207 & 0.327 & 0.305 & 0.330 \\  & Average & 0.228 & 0.187 & 0.299 & 0.282 & 0.305 \\ \hline \multirow{4}{*}{**Tail**} & Head & 0.054 & 0.059 & 0.129 & 0.128 & 0.145 \\  & Tail & 0.007 & 0.046 & 0.170 & 0.160 & 0.180 \\ \cline{1-1}  & Average & 0.030 & 0.052 & 0.149 & 0.144 & 0.162 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Experimental results for _FB15K data set_.