# Hypergraph-Clustering Method Based on an Improved Apriori Algorithm
## 5 Conclusions and Discussion  
This paper mainly focuses on clustering multi-dimensional datasets using a constructed hypergraph model. We propose a hypergraph-clustering method called HDHPA (high-dimensional data clustering method based on hypergraph partitioning using improved Apriori algorithm). The method starts by reducing the dimensionality of high-dimensional data and then performs clustering based on the hypergraph model. During the construction of the hypergraph, based on the knowledge of hypergraph theory, the traditional associative Apriori algorithm was improved. The HDHPA method uses parallel computing to eliminate the limitations of the Apriori algorithm in the iterative search of candidate sets, algorithm efficiency, and other aspects. The HDHPA can also reasonably measure the similarity between data in high-dimensional space. Then, using the dense subgraph segmentation DSP algorithm to segment the hypergraph can better merge similar dense subgraphs, it can improve clustering accuracy and obtain the final clustering result.  
Experiments were conducted on six protein-protein interaction (PPI) network datasets and the MNIST handwritten digit recognition dataset. The experimental results demonstrate that the HDHPA method outperforms traditional clustering algorithms and other hypergraph-partitioning algorithms, achieving efficient clustering results on datasets of different modalities. This indicates that the HDHPA method has broad applicability in various domains. Finally, the running time of all methods was compared, and the results show the superior performance of the HDHPA method in terms of time complexity. It is worth noting that the performance of our proposed method is related to the constructed hypergraph structure, so there are still many potential issues with the HDHPA method. Firstly, the method proposed in this paper has not yet comprehensively integrated more features of nodes and hyperedges into high-dimensional data to construct hypergraphs. Secondly, when improving the Apriori algorithm, how to reduce time complexity should be more comprehensive. Therefore, our future research directions mainly have two aspects: On the one hand, we will continue to try to conduct experiments on datasets in different fields, including high-dimensional network datasets such as social networks and brain networks. We will adjust the parameters of the method appropriately based on the characteristics of different modal datasets. On the other hand, combined with the latest intelligent clustering technology, we will further study how to shorten the running time mechanism of the method.  
Conceptualization, R.C. and F.H.; methodology, R.C., F.H., F.W. and L.B.; software, R.C.; validation, F.W., L.B. and F.H.; formal analysis, R.C., F.H. and L.B.; investigation, R.C. and F.W.; resources, L.B. and F.H.; writing--original draft preparation, R.C.; writing--review and editing, R.C., F.H. and L.B.; visualization, R.C.; supervision, F.H. and L.B. All authors have read and agreed to the published version of the manuscript.  
Figure 7: Comparison of FM-index and ARI values in all datasets.  
**Funding:** This paper was supported by the project: The National Natural Science Foundation of China (Grant No. 61663041) and the Basic Research Program of Qinghai Province (Grant No. 2023-ZJ-916M).  
**Institutional Review Board Statement:** Not applicable.  
**Data Availability Statement:** Not applicable.  
**Conflicts of Interest:** The authors declare no conflict of interest.