# Hypergraph-Clustering Method Based on an Improved Apriori Algorithm
## 4 Experiments and Analysis
### Experimental Comparison Results  
#### 4.6.1 Comparison of Experimental Results on PPI Networks  
This section applied five hypergraph-clustering methods to six protein-protein interaction network datasets of varying sizes. After clustering the selected datasets, we analyze their enrichment in GO terms associated with biological processes. The results are shown in Figure 5.  
Figure 5: Enrichment analysis of 6 protein–protein interaction network GO terms. In the enrichment analysis shown, the size of the circle represents the degree of significance of the enrichment and the color of the circle gradually decreases in significance from red to blue. Due to the small \(p\)-value, this paper chose the scale and color based on the \(-\log(P)\) value of each term's importance. Comparing six PPI network datasets, it can be seen from Figure 5 that they exhibit similar characteristics. GO terms that cluster more similarly to each other are also closer in space, and vertices with richer colors show changes in enrichment. Then, we summarized the information of six PPI network datasets, seen in in Table 3. We can see that the Natoc_0297 dataset has the highest average clustering coefficient, the HOXA10 dataset has the maximum average number of neighbors, the NNMT dataset has the highest network density, the 16 items dataset has the maximum value of network heterogeneity, and the NNMT dataset has the highest network centrality. According to the relevant theoretical knowledge of PPI networks [41], the clustering results of the Natoc_0297 and HOXA10 datasets are easier to distinguish. For the FAA4, 16 items, NNMT, and MBP datasets, there may be local optima in the clustering results of the dataset, but this situation is not within the scope of consideration. The evaluation indices FM-index and ARI values of the clustering results are summarized in Tables 4 and 5. As shown in Tables 4 and 5, For the FAA4 dataset, the FM-index value of the HDHPA method is higher than other methods, up to 0.805. The ARI value of the kD method is higher than other methods and is very close to the ARI value of the HDHPA method, far \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{5}{c}{**Dataset**} \\ \cline{2-6}  & **FAA4** & **Natoc\_0297** & **16 Items** & **HOXA10** & **NNMT** & **MBP** \\ \hline kh & 70.97 & 66.19 & 55.18 & 60.77 & 50.15 & 62.95 \\ kD & 77.80 & 74.16 & 50.29 & 51.40 & 46.64 & 61.01 \\ Ah & 44.14 & 47.51 & 24.34 & 38.51 & 19.33 & 49.20 \\ AD & 56.47 & 40.58 & 21.90 & 25.11 & 26.72 & 33.17 \\ HDHPA & 80.46 & 73.39 & 70.13 & 65.60 & 49.55 & 73.18 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: FM-index values of clustering results using 5 methods (unit %). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Dataset**} & **Avg.** & **Avg.** & **Network** & **Network** & **Network** \\  & **Clustering** & **Number of** & **Density** & **Heterogeneity** & **Centralization** \\  & **Coefficient** & **Neighbors** & & & \\ \hline FAA4 & 0.651 & 13.978 & 0.155 & 0.562 & 0.341 \\ Natoc\_0297 & 0.701 & 22.659 & 0.252 & 0.636 & 0.470 \\
16 items & 0.695 & 11.638 & 0.112 & 0.740 & 0.180 \\ HOXA10 & 0.630 & 44.596 & 0.297 & 0.584 & 0.489 \\ NNMT & 0.652 & 27.648 & 0.307 & 0.566 & 0.493 \\ MBP & 0.631 & 23.521 & 0.196 & 0.677 & 0.445 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary information of 6 protein–protein interaction networks. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{5}{c}{**Dataset**} \\ \cline{2-6}  & **FAA4** & **Natoc\_0297** & **16 Items** & **HOXA10** & **NNMT** & **MBP** \\ \hline kh & 77.62 & 74.50 & 34.98 & 56.97 & 46.95 & 67.06 \\ kD & 82.83 & 78.15 & 47.60 & 70.47 & 49.92 & 75.40 \\ Ah & 34.34 & 33.56 & 13.47 & 18.52 & 14.23 & 29.60 \\ AD & 58.67 & 50.91 & 38.12 & 46.33 & 58.95 & 48.71 \\ HDHPAexceeding other methods. In the Natoc_0297 dataset, the FM-index value of the kD method is higher than other methods.