# Cosine-Based Embedding for Completing Lightweight Schematic Knowledge in DL-Lite\({}_{core}\)+
## 5 Experiments and Results
### Case Study  
The above experiments show that CosE has good performances for link prediction and can preserve the logical properties of transitivity or symmetry well. Next, we present several concrete examples of completed results about CosE compared with TransE listed in Table 9, where the **bold** words show correct answers. We observe that CosE can improve the performance of predicting the tail concepts compared with TransE. The first example shows the result of predicting the tail concept of one \(subclassOf\) axiom. For TransE, the correct answer is ranked 35 th. The ranking of the correct answer in CosE has been significantly improved, and it is ranked fifth. It indicates that CosE could measure the confidences of axioms more precisely. Table 9 also shows the ability of CosE to preserve transitivity and symmetry. Compared with TransE, the second example shows that CosE improves the correct answer of a \(subclassOf\) axiom from 24 th to 4 th. Similarly, the correct answer of the disjointness axiom in the third example is improved to second place. These examples indicate that CosE can infer the tail or head concept more precisely than existing KG embedding models for given axioms. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{} & \multicolumn{6}{c}{**YAGO-On-t**} & \multicolumn{6}{c}{**YAGO-On-s**} \\ \hline \multirow{2}{*}{**Metric**} & \multicolumn{2}{c}{**MRR**} & \multicolumn{2}{c}{**Hits@N(\%)**} & \multicolumn{2}{c}{**MRR**} & \multicolumn{2}{c}{**Hits@N(\%)**} & \multirow{2}{*}{} \\  & **Raw** & **Filter** & **10** & **3** & **1** & **Raw** & **Filter** & **10** & **3** & **1** \\ \hline TransE [13] & 0.064 \(\dagger\) & 0.077 \(\dagger\) & 0.142 \(\dagger\) & 0.070 \(\dagger\) & 0.001 \(\dagger\) & 0.043 \(\dagger\) & **0.369 \(\dagger\)** & 0.971 \(\dagger\) & 0.514 \(\dagger\) & 0.080 \(\dagger\) \\ TransH [14] & 0.200 \(\dagger\) & 0.238 \(\dagger\) & 0.309 \(\dagger\) & 0.214 \(\dagger\) & 0.149 \(\dagger\) & 0.001 \(\dagger\) & 0.002 \(\dagger\) & 0.001 \(\dagger\) & 0.000 \(\dagger\) & 0.000 \(\dagger\) \\ TransR [15] & 0.012 \(\dagger\) & 0.013 \(\dagger\) & 0.003 \(\dagger\) & 0.002 \(\dagger\) & 0.001 \(\dagger\) & 0.010 \(\dagger\) & 0.010 \(\dagger\) & 0.001 \(\dagger\) & 0.000 \(\dagger\) & 0.000 \(\dagger\) \\ TransD [28] & 0.008 \(\dagger\) & 0.009 \(\dagger\) & 0.020 \(\dagger\) & 0.001 \(\dagger\) & 0.000 \(\dagger\) & 0.001 \(\dagger\) & 0.181 \(\dagger\) & 0.512 \(\dagger\) & 0.302 \(\dagger\) & 0.000 \(\dagger\) \\ RESCAL [16] & 0.016 \(\dagger\) & 0.020 \(\dagger\) & 0.055 \(\dagger\) & 0.015 \(\dagger\) & 0.004 \(\dagger\) & 0.032 \(\dagger\) & 0.166 \(\dagger\) & 0.449 \(\dagger\) & 0.226 \(\dagger\) & 0.039 \(\dagger\) \\ HolE [18] & 0.040 & 0.045 \(\dagger\) & 0.082 & 0.008 & 0.002 & **0.070** & 0.342 \(\dagger\) & 0.716 \(\dagger\) & 0.425 \(\dagger\) & **0.128** \\ Complex [19] & 0.001 \(\dagger\) & 0.001 \(\dagger\) & 0.001 \(\dagger\) & 0.000 \(\dagger\) & 0.000 \(\dagger\) & 0.036 \(\dagger\) & 0.253 \(\dagger\) & 0.743 \(\dagger\) & 0.439 \(\dagger\) & 0.000 \\ Analogy [47] & 0.001 \(\dagger\) & 0.001 \(\dagger\) & 0.001 \(\dagger\) & 0.001 \(\dagger\) & 0.000 \(\dagger\) & 0.043 \(\dagger\) & 0.315 \(\dagger\) & 0.932 \(\dagger\) & 0.538 \(\dagger\) & 0.000 \(\dagger\) \\ RotatE [23] & 0.001 & 0.001 \(\dagger\) & 0.001 \(\dagger\) & 0.000 & 0.000 & 0.002 \(\dagger\) & 0.002 \(\dagger\) & 0.001 \(\dagger\) & 0.000 \(\dagger\) & 0.000 \\ EL Embedding [24] & 0.001 & 0.001 & 0.001 & 0.001 & 0.000 & 0.000 & 0.003 \(\dagger\) & 0.003 \(\dagger\) & 0.075 \(\dagger\) & 0.017 \(\dagger\) & 0.003 \\ \hline CosE\({}^{-}\) & 0.203 & 0.260 & 0.403 & 0.246 & 0.177 & 0.038 & 0.322 & 0.983 \(\dagger\) & 0.554 \(\dagger\) & 0.000 \\ CosE & **0.207** & **0.284** & **0.408** & **0.261** & **0.218** & 0.038 & 0.323 & **0.992** & **0.557** & 0.000 \\ \hline \hline \end{tabular} \(\dagger\) Shows that the results are taken from the work [49]. Other results are obtained via their source codes.  
\end{table}