# Hypergraph-Clustering Method Based on an Improved Apriori Algorithm
## 4 Experiments and Analysis
### Experimental Comparison Results
#### 4.6.3 Running Time Comparison  
In this section, we compare the computational efficiency of hypergraph-clustering methods by comparing the running time complexity of all experiments. All experiments were conducted on the same server with the same configuration: Windows 10 Professional  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{2}{c}{**MNIST**} \\ \cline{2-3}  & **FM-Index** & **ARI** \\ \hline kh & 45.96 & 43.06 \\ kD & 46.52 & 48.40 \\ Ah & 63.97 & 57.24 \\ AD & 39.51 & 34.22 \\ HDHPA & 70.60 & 83.37 \\ \hline \hline \end{tabular}
\end{table}
Table 6: The clustering evaluation index of each method for MNIST dataset (unit %).  
OS, CUDA 11.6, Intel (R) Xeon (R) E-2244G CPU (4.80 GHz), Nvidia GeForce RTX 4070 Ti GPU (12 GB), mainly based on Python 3.8.13 as the development language support. PyCharm 2021.3.1 IDE implements a parallel computing environment. We will display the running time of five methods on six protein-protein interaction network datasets (FAA4, Natoc_0297, 16 items, HOXA10, NNMT, and MBP) and the MNIST handwritten digit recognition dataset (only the trained part is selected), as shown in Figure 6.  
From the results, the HDHPA method has an overall running time less than the other methods in all datasets, with a duration of less than 10 s. In the HOXA10 dataset, except for the HDHPA method, all other methods have a running time of more than 10 s, with a maximum running time of 18.4 s. The running time of all methods shows a consistent pattern. We can see that the speed of hypergraph-clustering methods can be ranked (from fastest to slowest) as HDHPA, kD, AD, kh, and Ah. We can see that using association rules to construct hypergraphs requires the iterative processing of complex and large-scale datasets in a non-parallel search regime, which leads to longer running time. Therefore, parallel search can significantly reduce the running time of processing large-scale data. By comparing only six PPI network datasets, it can see that HDHPA is more efficient than AD and Ah. Therefore, considering both running time and classification accuracy, the HDHPA is more competitive.  
Based on the values of clustering evaluation indicators in the experimental results, the next step is to discuss clustering efficiency. From Figure 7, the clustering efficiency of the AD method will change significantly with the characteristics of the datasets, and the Ah method is generally lower than other methods in clustering evaluation indicators. The FM-index and ARI values of the HDHPA method are substantially higher than other methods, and the highest values can be close to 0.9. Therefore, the HDHPA method has lower time costs and more stable performance on different datasets. Because the construction and partition of the hypergraph occupy most of the running time, the improvement of the traditional Apriori algorithm makes the construction of the hypergraph a parallel calculation, saving a lot of time and achieving a better trade-off between effectiveness and efficiency.  
Figure 6: Comparison of run times of different methods on different datasets.