## 4 Results
### Experiment Results  
The experimental results demonstrate that PDEC possesses the capability to perform predicate inductive KGC tasks through predicate decomposition, and the original predicate set can be effectively restored using Equation (8), leading to an enhancement in the reasoning performance for the original transductive KGC task. In the subsequent sections, we will present comprehensive experimental results showcasing PDEC's impact on improving the reasoning performance of the original KGC task. These results cover various benchmarks and large datasets, i.e., drug rediscovery. Furthermore, we will demonstrate the correlation between the granularity of predicate decomposition and the corresponding performance improvements. Lastly, we will evaluate the influence of synonymous predicate merging on the overall performance of the KGC task. **The KGC performance improvement on benchmarks brought by PDEC**. We tested the performance of the baseline reasoning model on FB15K-237, YAGO3-10, and NELL-995, as well as the performance improvement of PDEC, as shown in the Table 1. The initial edge vectors are generated using TransE. We performed PDEC using Algorithm 1, resulting in datasets with new predicates. All tests ensure that the reasoning model keeps hyperparameters unchanged during the testing of the original benchmark and the benchmark after PDEC to ensure a fair comparison. The results indicate that PDEC can effectively promote the performance of KG reasoning models. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multirow{2}{*}{**PDEC**} & \multicolumn{4}{c}{**FB15K-237**} & \multicolumn{4}{c}{**YAGO3-10**} & \multicolumn{4}{c}{**NELL-995**} \\ \cline{2-11}  & & **MRR** & **Hits@1** & **Hits@3** & **Hits@10** & **MRR** & **Hits@1** & **Hits@3** & **Hits@10** & **MRR** & **Hits@1** & **Hits@3** & **Hits@10** \\ \hline \multirow{2}{*}{TransE} & ✘ & 0.289 & 19.3 & 32.6 & 47.9 & 0.330 & 21.5 & 38.8 & 54.9 & 0.252 & 9.64 & 38.5 & 47.2 \\  & ✔ & **0.349** & **24.24** & **39.9** & 58.8 & **0.395** & **28.0** & **46.0** & **60.3** & **0.287** & **11.7** & **43.0** & **52.7** \\ \hline \multirow{2}{*}{DistMult} & ✘ & 0.187 & 10.3 & 20.7 & 36.1 & 0.073 & 2.93 & 6.87 & 16.7 & 0.163 & 7.10 & 19.1 & 33.9 \\  & ✔ & **0.224** & **13.3** & **25.4** & **40.9** & **0.112** & **3.93** & **12.0** & **28.5** & **0.186** & **9.0** & **21.6** & **35.4** \\ \hline \multirow{2}{*}{TransH} & ✘ & 0.260 & 18.4 & 32.9 & 48.4 & 0.332 & 22.1 & 38.9 & 54.4 & 0.255 & 10.0 & 39.6 & 48.8 \\  & ✔ & **0.314** & **20.6** & **36.1** & **52.2** & **0.385** & **26.6** & **43.7** & **62.2** & **0.278** & **13.5** & **40.7** & **51.6** \\ \hline \multirow{2}{*}{RotatE} & ✘ & 0.321 & 22.8 & 35.6 & 50.6 & 0.270 & 17.9 & 30.3 & 44.6 & 0.368 & 31.4 & 40.5 & 45.6 \\  & ✔ & **0.360** & **26.4** & **40.2** & **54.7** & **0.355** & **25.6** & **39.8** & **54.3** & **0.374** & **32.1** & **41.1** & **46.0** \\ \hline \multirow{2}{*}{TransR} & ✘ & 0.305 & 20.8 & 34.4 & 49.6 & 0.321 & 11.6 & 48.6 & 0.37 & 26.1 & 10.8 & 39.4 & 49.0 \\  & ✔ & **0.334** & **23.5** & **37.8** & **53.3** & **0.496** & **39.2** & **56.0** & **68.3** & **0.276** & **11.7** & **41.0** & **53.3** \\ \hline \multirow{2}{*}{TransD} & ✘ & 0.254 & 18.1 & 32.7 & 46.6 & 0.323 & 21.5 & 35.9 & 53.8 & 0.263 & 10.5 & 39.9 & 50.1 \\  & ✔ & **0.310** & **20.0** & **36.1** & **51.9** & **0.377** & **25.1** & **42.6** & 61.7 & **0.280** & **12.1** & **40.4** & **50.8** \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The performance gain of PDEC on baseline models in benchmark experiments. Hits@k is in %. The KGC performance improvement brought by PDEC on a large-scale dataset (i.e., drug rediscovery).We conducted KGC experiments on the large-scale biochemical knowledge graph RTX-KG2c and compared the performances of the baseline model before and after applying the PDEC framework.