# Hypergraph-Clustering Method Based on an Improved Apriori Algorithm
## 1 Introduction  
With the explosive growth of information, the huge amount of data generated [1] has permeated every industry and field. Moreover, most of these data presented high dimensions and complex structures. How to handle these massive and complex data has become an urgent challenge in the field of machine learning at present. Clustering is one of the most important methods in machine learning, which reasonably assigns data into a cluster by selecting a measurement method [2]. Traditional clustering methods are mainly using classical machine learning theoretical knowledge to conduct research, such as partition-based clustering methods [3] and hierarchy-based clustering methods [4], etc. With the progression of time, although many scholars improve the traditional clustering algorithm on this basis, due to the special characteristics of complex data, they often cannot achieve ideal clustering results, which is mainly reflected in poor clustering divisionresults [5]. Due to the fact that the graph-based data analysis method can identify well-connected vertices clusters [6], this makes up for the shortcomings of ordinary high-dimensional data clustering. Therefore, clustering analysis through graphs has become a more common processing method. However, ordinary graphs cannot comprehensively describe various complex relationships in data, such as the World Wide Web, airline networks, etc. These networks often have intricate internal structures [7; 8; 9; 10]. Inspired by this, hypergraphs have emerged. Hypergraphs [11] are mainly used to study the generalization of multiple relationships in graph topology structures and are widely used in many fields of information technology. One popular direction is to use hypergraphs for clustering analysis [12] and to effectively represent high-order correlations between data in a visualized form using hypergraphs [13]. In the contemporary period, many new clustering algorithms have been proposed to handle complex data by constructing hypergraphs. [PERSON] et al. [14] transformed the clustering problem into a hypergraph-partitioning combinatorial optimization problem, and proposed three consensus functions for better clustering. [PERSON] et al. [15] systematically discussed cluster ensembles, compared the advantages and disadvantages of traditional clustering algorithms, and extended their analysis to hypergraph partitioning. Based on the evolutionary model of the hypernetwork dynamics process, [PERSON] et al. [16] provided a comprehensive overview of the future development directions in the field of hypergraphs. [PERSON] et al. [17] introduced knowledge hypergraphs using heterogeneous hypergraphs, constructed a three-layer architecture to better represent and extract hyper-featured relationships, and modeled hyper-relation data. [PERSON] et al. [18] constructed a hypergraph to embed sample representation and proposed an optimized constrained clustering algorithm with upper and lower limits on the number of clusters. All these studies have demonstrated the superiority and universality of hypergraph-clustering methods. Due to the complexity and variability of today's data, it is still necessary to adopt more scientific and objective methods in constructing hypergraphs. Association rules are commonly used, as they can acquire frequent itemsets and association rules to clarify the relationships between data. [PERSON] et al. [19] proposed the HOT algorithm combining outlier detection based on the hypergraph model and association rules to calculate the support degree, membership degree, and other information for each point. However, it may suffer from local optima issues. [PERSON] et al. [20] comprehensively discussed several applications of hypergraphs in data mining, including association rules, clustering, and spatial data mining. [PERSON] et al. [21] constructed a hypergraph model and investigated the association relationships in hypergraphs based on the hypergraph-partitioning algorithm hMETIS and the association rule algorithm Apriori.