## 4 Experimental Evaluation
### Wikipedia Dataset
#### 4.2.4 Impact of \(d\) on Accuracy of Embedding Methods  
In this section, we analyze whether _increasing_ the number of dimensions _improves_ the effectiveness of embedding methods in computing the similarity of nodes. In Section 4.2.2, Figure 4 illustrates the accuracy of all embedding methods with the BlogCatalog, Cora, and DBLP datasets for different values of \(d\); in addition, Figure 5 illustrates the results of the same experiments with the TREC and Wikipedia datasets. As observed in these figures, in some cases such as DWNS and NetMF with the BlogCatalog dataset, increasing the number of dimensions _improves_ the accuracy of the embedding methods (i.e., refer to Figure 4); on the contrary, in some cases such as Line with the Wikipedia dataset (i.e., refer to Figure 5) and graphGAN with the BlogCatalog dataset (i.e., refer to Figure 4), increasing the number of dimensions _adversely_ affects the accuracy of the embedding methods. In addition, in some cases such as DeepWalk with the DBLP dataset (i.e., refer to Figure 4) and node2 vec with the TREC dataset (i.e., refer to Figure 5), we observe _both_ improvement and reduction in accuracy by increasing the number of dimensions. In summary, increasing the value of \(d\) does _not_ help improve the accuracy of embedding methods in computing the similarity of nodes. In Section 4.2.2, Table 3 indicates the value of \(d\) showing the best accuracy for each embedding method with our datasets. As represented in Table 3, some embedding methods show their best accuracies when \(d=64\) or \(d=512\); we call such a case a _suspicious_ one since it _may_ possible to improve the accuracy of the embedding method by assigning a lower (i.e., 32) or higher (i.e., 1024) value to \(d\), respectively. However, if the accuracy of a suspicious case is _not_ comparable with the accuracy of the _best_ method in the dataset, conducting the aforementioned experiment is _not_ beneficial since our overall observations will not be affected by the new result; for example, although ATP with the BlogCatalog dataset shows its highest accuracy when \(d=512\) as a suspicious case, its accuracy is _quite_ lower than that of NetMF as the best method for the same dataset (refer to Figure 6). In Table 3, there are _only_ four following real suspicious \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & **ATP** & **BoostNE** & **DeepWalk** & **DWNS** & **graphGAN** & **Line** & **NERD** & **NetMF** & **node2 vec** & **SimRank*** & **SimRank** \\ \hline MAP & 458.30 & 502.50 & 140.20 & 168.77 & 1663.41 & 179.69 & 557.27 & 161.48 & 330.36 & 347.68 & 1125.42 \\ precision & 80.82 & 72.57 & 34.91 & 61.70 & 112.21 & 24.10 & 54.15 & 33.68 & 43.00 & 90.86 & 85.06 \\ recall & 405.74 & 204.50 & 74.16 & 54.05 & 593.77 & 98.22 & 354.20 & 105.76 & 242.50 & 82.38 & 702.54 \\ PRES & 372.19 & 266.90 & 83.45 & 91.50 & 913.74 & 114.11 & 375.33 & 105.08 & 247.24 & 181.82 & 762.50 \\ F-score & 252.98 & 212.50 & 66.55 & 156.61 & 588.92 & 83.30 & 238.21 & 68.29 & 166.48 & 151.56 & 420.39 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Accuracy improvements (%) by JacSim over other methods with the Wikipedia dataset. Figure 10: Accuracy of embedding methods and similarity measures with the Wikipedia dataset. cases that we need to consider them: both DeepWalk and Line show their highest accuracies when \(d=512\) with the Cora dataset and their accuracies are very close to that of JPRank as the best method with Cora (i.e., refer to Figure 7). In addition, DeepWalk and NetMF show their highest accuracies when \(d=64\) and \(d=512\) with the TREC dataset, respectively; their accuracies are very close to that of SimRank* as the best method with TREC (i.e., refer to Figure 9). Therefore, we conduct the following four new experiments:  
1. DeepWalk with the Cora dataset and \(d=1024\)
2. Line with the Cora dataset and \(d=1024\)
3. DeepWalk with the TREC dataset and \(d=32\)
4.