• 대한수학회논문집
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• 제38권1호
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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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• 제17권4호
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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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• 제17권11호
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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.

• 정보과학회 컴퓨팅의 실제 논문지
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• 제23권8호
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• pp.492-497
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• 2017

하이퍼그래프는 노드와 여러 노드를 연결할 수 있는 하이퍼에지로 구성된다. 하이퍼그래프 분석을 위해 그래프 기본 연산 중 그래프 탐색을 사용할 수 있다. 일반 그래프에 사용되는 DFS, BFS 탐색방법을 하이퍼그래프에 그대로 적용하였을 시 여러 노드를 연결하는 하이퍼에지의 특성을 고려하지 않는 문제가 있다. 본 논문에서는 하이퍼그래프를 위한 DBMS인 hypergraphDB에 저장 된 그래프 탐색 시 에지 단위로 탐색 여부를 판단하는 방법을 제안하고, 제안 탐색 방법을 응용한 하이퍼그래프 분석 실험을 수행하였다. 실험을 통해 일반 그래프의 탐색 기법을 적용한 경우 보다 빠른 속도와 보다 적은 DB 접근 횟수로 그래프 분석 작업을 수행함을 보인다.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제13권2호
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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.

• 한국지능시스템학회논문지
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• 제4권2호
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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.

• 산업경영시스템학회지
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• 제24권65호
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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.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 1998년도 The Third Asian Fuzzy Systems Symposium
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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.

• 한국정보과학회논문지:소프트웨어및응용
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• 제26권2호
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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.

• 한국지능시스템학회논문지
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• 제24권2호
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• pp.166-172
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• 2014

이미지를 각각의 카테고리로 분류하는 일은 컴퓨터 비전 분야의 중요한 문제 중 하나이다. 그러나 이미지에 존재하는 가변성, 모호성, 스케일 문제 등으로 인해 매우 도전적인 문제라고 할 수 있다. 본 논문에서는 장면 이미지를 구성하는 시멘틱 속성들의 고차원의 상호작용 관계를 고려 가능한 하이퍼그래프 기반의 모델링 기법을 제시하고 이를 장면 이미지 분류에 적용한다. 각 장면 카테고리에 준최적화된 하이퍼그래프를 생성하기 위해 확률 부분공간 기법에 기반을 둔 탐색기법을 제안하고, 이들 부분 공간 내에 속한 시멘틱 속성들의 발현량을 축약하기 위한 우도비 기반의 선형 변환 기법을 제안한다. 제안한 기법의 우수성을 검증하기 위한 실험을 통하여 제시한 기법을 통해 생성된 특징 벡터의 분별력이 기존의 기법들에서 사용된 특징 벡터들의 분별력보다 우수함을 보인다. 또한 제안한 기법을 장면 분류 데이터에 적용한 결과 기존의 기법들과 비교하여 경쟁력 있는 분류 성능을 보인다. 제안 한 기법은 이미지 분류에서 일반적으로 사용 되는 기법인 BoW+SPM 모델과 비교하여 3~4%이상의 성능 향상을 보였다.