## 4 Experimental Evaluation
### Semantic Clustering Performance  
We measured the semantic clustering performance by employing Recall (\(R\)), Precision (\(P\)), and F-measure (\(F\)). The measure \(R\) is a measure of completeness, whereas \(P\) is a measure of exactness or fidelity. An inverse relationship exists between \(R\) and \(P\) wherein it is possible to increase only one at the cost of reducing the other. Usually, \(R\) and \(P\) measures are not discussed in isolation; both are combined into a single measure, such as \(F\), which is the weighted harmonic mean of \(R\) and \(P\). We consider these measures for semantic search. Let \(\Omega\) be the set of relevant resources, \(C\) (correct) be the number of returned relevant resources, \(I\) (incorrect) be the number of returned irrelevant resources, and \(M\) (missing) be the number of missing relevant resources. We define:  
\[R=\frac{C}{C+M}P=\frac{C}{C+I}\text{ and }F=\frac{2P\times R}{P+R} \tag{5}\]  
where the size of \(\Omega\) is equal to \(C+M\).  
Table 2 and Figure 7 enumerate the semantic clustering performance for various embedding methods in the case of random semantic search. We conducted an additional experiment focusing on the performance of clustering algorithms, such as DBSCAN and \(K\)-means. The \(K\)-means clustering algorithm is mainly applicable to spherically distributed data. The experiment results showed that the translation-based models--TransE and TransR--were better than the bilinear-based models--RESCAL, DistMult, and complex--and the neural network-based model--ConvE. In particular, our LearnS demonstrates excellent performance on \(P\), \(R\), and \(F\). The main reason is that this model solves the problem of annotation heterogeneity by projecting entities from entity space to corresponding relation space and applying the density-based spatial clustering algorithm. In general, there was an inverse relationship between recall and precision. In Figure 7, however, TransH, RESCAL, DistMult, and complex show poor results for both. This figure shows that ConvE also has a slightly poor performance in these measures. Although the ConvE model has shown its superiority in knowledge graph completion by using two-dimensional convolution techniques to extract the feature vector of triples, the semantic clustering effect is unsatisfactory. From Table 2, we can also observe that the DBSCAN method exhibit better performance than the \(K\)-means method. Figure 8 shows that all LUMB data are converted into the three-dimensional space. The TransR and LearnS models showed the excellent clustering performance compared with other methods.  
Figure 6: Building time for various index structures. (**a**) LUBM dataset, (**b**) LinkedGeoData dataset.  
\begin{table}
\begin{tabular}{l c c c} \hline \hline \multirow{2}{*}{**Models**} & **Precision (P)** & **Recall (R)** & **F-Measure (F)** \\  & **DBSCAN (K-Means)** & **DBSCAN (K-Means)** & **DBSCAN (K-Means)** \\ \hline TransE & 0.335 (0.250) & 0.903 (0.865) & 0.489 (0.388) \\ TransH & 0.130 (0.060) & 0.240 (0.080) & 0.168 (0.068) \\ TransR & 0.365 (0.340) & 0.955 (0.901) & 0.511 (0.402) \\ RESCAL & 0.280 (0.250) & 0.220 (0.182) & 0.246 (0.210) \\ DistMult & 0.210 (0.334) & 0.160 (0.287) & 0.182 (0.308) \\ complex & 0.325 (0.310) & 0.221 (0.268) & 0.263 (0.287) \\ ConvE & 0.340 (0.335) & 0.480 (0.425) & 0.398 (0.375) \\ LearnS & 0.386 (0.345) & 0.970 (0.930) & 0.552 (0.503) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Evaluation of semantic clustering performance.  
Figure 7: Semantic clustering performance based on DBSCAN and _K_-means. (**a**) Semantic clustering performance based on DBSCAN. (**b**) Semantic clustering performance based on _K_-means.  
Figure 8: Visualization of the embedded LUMB dataset. (**a**) TransE, (**b**) TransH, (**c**) TransR, (**d**) RESCAL, (**e**) Complex, (**f**) DistMult, (**g**) ConvE, (**h**) LearnS.