# An Approach to Knowledge Base Completion
## 4 Committee-Based Knowledge Base Completion  
This paper proposes committee-based knowledge base completion that adopts a committee of knowledge graph embeddings to measure the plausibility of candidate missing triples. Figure 1 shows how the set of missing triples, \(T\), is found systematically by the proposed committee-based knowledge base completion method. The proposed method first generates \(\mathbf{C}_{cand}\), a set of candidate missing triples from \(S\) as in the work of [PERSON] et al. [35]. Let \(C_{h}\) be a concept of \(h\), \(C_{t}\) be that of \(t\), \(H_{h}\) be a set of all entities belonging to \(C_{h}\), and \(T_{t}\) be a set of all entities belonging to \(C_{t}\). Then, from every triple \(\langle h,r,t\rangle\in S\), the candidate triples are generated by replacing \(h\) with one of the elements in \(H_{h}\) except \(h\) or replacing \(t\) with one of the elements in \(T_{t}\) but \(t\). Thus, \((|H_{h}|-1)\cdot(|T_{t}|-1)\) candidates are prepared from each triple in \(S\). Once \(\mathbf{C}_{cand}\) is prepared, all its members are sorted according to their plausibility. There could be a number of ways to compute the plausibility of candidate triples, but knowledge graph embeddings are adopted to compute the plausibility in this paper. A knowledge graph embedding represents all entities and relations in \(S\) as low-dimensional vectors thereby preserving the inherent structure of \(S\). Since the embedding is trained to preserve the structure of its knowledge graph, it can be used to measure how plausible the embedded vectors are in the space spanned by the knowledge graph embedding. Even if any knowledge graph embedding can be used to compute the plausibility of triples, every embedding has its own idiosyncrasy. Table 2 proves this. This table shows the top-10 candidate tail entities suggested by four famous knowledge graph embeddings when a head entity \(yogurt\) and a relation \(hypernym\) are known. The knowledge graph embeddings used in this table are TransE, TransR, DistMult, and ComplEx, and the entities are the synsets in the WordNet knowledge base. The bold entities are correct tail entities for \(yogurt\) and \(hypernym\) (Multiple entities can be correct since the relation \(hypernym\) is transitive), and the shaded entities are those shared at least by two embeddings. As shown in this table, different knowledge graph embeddings suggest different entities. TransE shares three entities _dairy product_, _solid food_, and _foodstuff_ out of ten with TransR, and two entities of dairy product_ and _solid food_ with DistMult and ComplEx. Moreover, even the shared entities are ranked differently. For instance, _dairy product_ is ranked first by TransE, fifth by TransR, ninth by DistMult, and second by ComplEx, while _solid food_ is ranked second, third, sixth, and first by them. The ranking differences according to different embedding can be shown numerically by _[PERSON]'s rank correlation coefficient_, which is a widely-used metric to evaluate rank correlation. Table 3 shows the [PERSON]'s rank correlation coefficient between different knowledge graph embeddings. These coefficients are obtained using 500 triples sampled from the development set of WN18 dataset [6]. The average coefficient among the embeddings is 0.5158. The coefficient between TransE and TranR is highest as 0.5904, and that between TransR and DistMult is lowest as 0.4916. These values prove that the embeddings are positively related, but not that strongly related. DistMult, in particular, shows lower coefficients against other embeddings, which implies that it ranks entities differently from the others. In order to reflect the idiosyncrasies of knowledge graph embeddings in knowledge base completion while maximizing their effectiveness, the proposed method computes the plausibility of triples by a committee of knowledge graph embeddings rather than by a single knowledge graph embedding. That is, the plausibility of a candidate triple in \(\mathbf{C}_{cand}\) is determined by the committee of knowledge graph embeddings.