• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.55-67
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• 2023

In this paper we obtain a new structure of a k-annihilating ideal hypergraph of a reduced ring R, by determine the order and size of a hypergraph 𝒜𝒢_k(R). Also we describe and count the degree of every nontrivial ideal of a ring R containing in vertex set 𝒜(R, k) of a hypergraph 𝒜𝒢_k(R). Furthermore, we prove the diameter of 𝒜𝒢_k(R) must be less than or equal to 2. Finally, we determine the minimal dominating set of a k-annihilating ideal hypergraph of a ring R.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.17 no.4
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• pp.1182-1199
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• 2023

Fractional repetition (FR) codes can achieve exact uncoded repair for multiple failed nodes, with lower computational complexity and bandwidth overhead, and effectively improve repair performance in distributed storage systems (DSS). The actual distributed storage system is dynamic, that is, the parameters such as node storage overhead and number of storage nodes will change randomly and dynamically. Considering that traditional FR codes cannot be flexibly applied to dynamic distributed storage systems, a new construction scheme of adaptive-and-resolvable FR codes based on hypergraph coloring is proposed in this paper. Specifically, the linear uniform regular hypergraph can be constructed based on the heuristic algorithm of hypergraph coloring proposed in this paper. Then edges and vertices in hypergraph correspond to nodes and coded packets of FR codes respectively, further, FR codes is constructed. According to hypergraph coloring, the FR codes can achieve rapid repair for multiple failed nodes. Further, FR codes based on hypergraph coloring can be generalized to heterogeneous distributed storage systems. Compared with Reed-Solomon (RS) codes, simple regenerating codes (SRC) and locally repairable codes (LRC), adaptive-and-resolvable FR codes have significant advantages over repair locality, repair bandwidth overhead, computational complexity and time overhead during repairing failed nodes.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.17 no.11
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• pp.2903-2923
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• 2023

Knowledge recommendation is a type of recommendation system that recommends knowledge content to users in order to satisfy their needs. Although using graph neural networks to extract data features is an effective method for solving the recommendation problem, there is information loss when modeling real-world problems because an edge in a graph structure can only be associated with two nodes. Because one super-edge in the hypergraph structure can be connected with several nodes and the effectiveness of knowledge graph for knowledge expression, a dual-channel hypergraph convolutional neural network model (DCHC) based on hypergraph structure and knowledge graph is proposed. The model divides user data and knowledge data into user subhypergraph and knowledge subhypergraph, respectively, and extracts user data features by dual-channel hypergraph convolution and knowledge data features by combining with knowledge graph technology, and finally generates recommendation results based on the obtained user embedding and knowledge embedding. The performance of DCHC model is higher than the comparative model under AUC and F1 evaluation indicators, comparative experiments with the baseline also demonstrate the validity of DCHC model.

• KIISE Transactions on Computing Practices
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• v.23 no.8
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• pp.492-497
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• 2017

A hypergraph consists of a set of nodes and hyperedges that connect an arbitrary number of nodes. We employ graph traversal algorithms such as BFS and DFS to analyze or explore hypergraph data. However, the conventional BFS and DFS do not consider the structural characteristics of hyperedges. In this paper, we propose a method to record visited edges and nodes during the traversal algorithm for data stored in hypergraphDB. In the experiments, we conduct various hypergraph analyses that utilize traversal algorithms and show that our method achieves a fewer number of database accesses and faster processing time than the conventional one.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.13 no.2
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• pp.494-513
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• 2019

A multi-channel access problem based on hypergraph model in ultra-dense small cell networks is studied in this paper. Due to the hyper-dense deployment of samll cells and the low-powered equipment, cumulative interference becomes an important problem besides the direct interference. The traditional binary interference model cannot capture the complicated interference relationship. In order to overcome this shortcoming, we use the hypergraph model to describe the cumulative interference relation among small cells. We formulate the multi-channel access problem based on hypergraph as two local altruistic games. The first game aims at minimizing the protocol MAC layer interference, which requires less information exchange and can converge faster. The second game aims at minimizing the physical layer interference. It needs more information interaction and converges slower, obtaining better performance. The two modeled games are both proved to be exact potential games, which admit at least one pure Nash Equilibrium (NE). To provide information exchange and reduce convergecne time, a cloud-based centralized-distributed algorithm is designed. Simulation results show that the proposed hypergraph models are both superior to the existing binary models and show the pros and cons of the two methods in different aspects.

• Journal of the Korean Institute of Intelligent Systems
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• v.4 no.2
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• pp.3-8
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• 1994

In this paper, the hypergraph is fuzzified. In a hypoergraph, there are 3types of sets which can be fuzzified. According to the fuzzificatioin level, 7 types of fuzzy hypergraphs can be obtained. After defining the 7 thpes of hypergraphs, some interesting concepts are developed such as the order, size and degree of such as the order, size and degree of the fuzzy hypergraph.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.24 no.65
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• pp.41-50
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• 2001

Clustering in data mining is a discovery process that groups a set of data such that the intracluster similarity is maximized and intercluster similarity is minimized. The discovered clusters from clustering process are used to explain the characteristics of the data distribution. In this paper we propose a new methodology for clustering related transactions with categorical attributes. Our approach starts with transforming general relational databases into a transactional databases. We make use of inter-dimensional association rules for composing hypergraph edges, and a hypergraph partitioning algorithm for clustering the values of attributes. The clusters of the values of attributes are used to find the clusters of transactions. The suggested procedure can enhance the interpretation of resulting clusters with allocated attribute values.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.549-551
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• 1998

For a fuzzy system modeled by a fuzzy hypergraph, two fuzzy similarity measures are proposed : one for the fuzzy similarity between fuzzy sets and the other between elements in fuzzy sets. The propose measures can represent the realistic similarities which can not be given by the existing measures. With and example, it is shown that it can be used in the behavior analysis in an organization.

• Journal of KIISE:Software and Applications
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• v.26 no.2
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• pp.321-333
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• 1999

본 논문은 퍼지 하이퍼그래프(fuzzy hypergraph)를 확장하여 타입-2 퍼지 하이퍼그래프를 정의하고, 이렇게 정의된 그래프의 듀얼( dual)을 소개한다. 그리고 하이퍼그래프의 시스템 분석력을 증대시키기 위하여 원소와 에지(edge)의 인접한 정도를 나타내는 인접도(adjavent level)를 확장하여 퍼지 인접도를 정의한다. 이와 같이 정의된 인접도를 새로이 정의된 타입-2 퍼지 하이퍼그래프에 적용하여 하이퍼그래프의 시스템 분석능력을 증대시킴을 보인다.

• Journal of the Korean Institute of Intelligent Systems
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• v.24 no.2
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• pp.166-172
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• 2014

Image classification is an important problem in computer vision. However, it is a very challenging problem due to the variability, ambiguity and scale change that exists in images. In this paper, we propose a method of a hypergraph based modeling can consider the higher-order relationships of semantic attributes of a scene image and apply it to a scene image classification. In order to generate the hypergraph optimized for specific scene category, we propose a novel search method based on a probabilistic subspace method and also propose a method to aggregate the expression values of the member semantic attributes that belongs to the searched subsets based on a linear transformation method via likelihood based estimation. To verify the superiority of the proposed method, we showed that the discrimination power of the feature vector generated by the proposed method is better than existing methods through experiments. And also, in a scene classification experiment, the proposed method shows a competitive classification performance compared with the conventional methods.