• KSII Transactions on Internet and Information Systems (TIIS)
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• 제9권7호
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• pp.2568-2584
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• 2015

Spectral clustering has become one of the most popular clustering approaches in recent years. Similarity graph constructed on the data is one of the key factors that influence the performance of spectral clustering. However, the similarity graphs constructed by existing methods usually contain some unreliable edges. To construct reliable similarity graph for spectral clustering, an efficient method based on Markov random walk (MRW) is proposed in this paper. In the proposed method, theMRW model is defined on the raw k-NN graph and the neighbors of each sample are determined by the probability of the MRW. Since the high order transition probabilities carry complex relationships among data, the neighbors in the graph determined by our proposed method are more reliable than those of the existing methods. Experiments are performed on the synthetic and real-world datasets for performance evaluation and comparison. The results show that the graph obtained by our proposed method reflects the structure of the data better than those of the state-of-the-art methods and can effectively improve the performance of spectral clustering.

• 대한수학회지
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• 제54권4호
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• pp.1121-1148
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• 2017

Go is an ancient game of great complexity and has a huge following in East Asia. It is also very rich mathematically, and can be played on any graph, although it is usually played on a square lattice. As with any game, one of the most fundamental problems is to determine the number of legal positions, or the probability that a random position is legal. A random Go position is generated using a model previously studied by the author, with each vertex being independently Black, White or Uncoloured with probabilities q, q, 1 - 2q respectively. In this paper we consider the probability of legality for two scenarios. Firstly, for an $N{\times}N$ square lattice graph, we show that, with $q=cN^{-{\alpha}}$ and c and ${\alpha}$ constant, as $N{\rightarrow}{\infty}$ the limiting probability of legality is 0, exp($-2c^5$), and 1 according as ${\alpha}$ < 2/5, ${\alpha}=2/5$ and ${\alpha}$ > 2/5 respectively. On the way, we investigate the behaviour of the number of captured chains (or chromons). Secondly, for a random graph on n vertices with edge probability p generated according to the classical $Gilbert-Erd{\ddot{o}}s-R{\acute{e}}nyi$ model ${\mathcal{G}}$(n; p), we classify the main situations according to their asymptotic almost sure legality or illegality. Our results draw on a variety of probabilistic and enumerative methods including linearity of expectation, second moment method, factorial moments, polyomino enumeration, giant components in random graphs, and typicality of random structures. We conclude with suggestions for further work.

• 한국전자거래학회지
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• 제20권2호
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• pp.155-166
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• 2015

랜덤워크는 그래프 기반의 랭킹 기법들에서 빈번히 사용되지만, 그래프 간선에 음수 가중치를 가지는 부호 그래프는 고려하지 않는다. 이 논문에서는 하이더의 균형 이론을 적용하여 랜덤워크수행 시 음수 가중치를 처리하는 기법을 제안한다. 제안 기법은 추천 시스템에 적용되었으며, 사용자가 선호하지 않는 아이템을 걸러내는 데 효과가 있음을 실험을 통해 보인다. 제안한 모델의 성능을 위해 기존의 Top-k 랜덤워크 계산 기법인 BCA를 확장한 Bicolor-BCA 알고리즘을 제안한다. 제안 알고리즘은 임계값이 필요한데, 실험을 통해 임계값에 따른 정확도와 성능의 변화를 살펴본다.

• 대한수학회지
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• 제60권2호
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• pp.255-271
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• 2023

In this paper, we deal with random attractors for dynamical systems forced by a deterministic noise. These kind of systems are modeled as skew products where the dynamics of the forcing process are described by the base transformation. Here, we consider skew products over the Bernoulli shift with the unit interval fiber. We study the geometric structure of maximal attractors, the orbit stability and stability of mixing of these skew products under random perturbations of the fiber maps. We show that there exists an open set U in the space of such skew products so that any skew product belonging to this set admits an attractor which is either a continuous invariant graph or a bony graph attractor. These skew products have negative fiber Lyapunov exponents and their fiber maps are non-uniformly contracting, hence the non-uniform contraction rates are measured by Lyapnnov exponents. Furthermore, each skew product of U admits an invariant ergodic measure whose support is contained in that attractor. Additionally, we show that the invariant measure for the perturbed system is continuous in the Hutchinson metric.

• Earthquakes and Structures
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• 제10권1호
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• pp.25-51
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• 2016

In this study, graph product rules are applied to the dynamic analysis of regular skeletal structures. Graph product rules have recently been utilized in structural mechanics as a powerful tool for eigensolution of symmetric and regular skeletal structures. A structure is called regular if its model is a graph product. In the first part of this paper, the formulation of time history dynamic analysis of regular structures under seismic excitation is derived using graph product rules. This formulation can generally be utilized for efficient linear elastic dynamic analysis using vibration modes. The second part comprises of random vibration analysis of regular skeletal structures via canonical forms and closed-form eigensolution of matrices containing special patterns for symmetric structures. In this part, the formulations are developed for dynamic analysis of structures subjected to random seismic excitation in frequency domain. In all the proposed methods, eigensolution of the problems is achieved with less computational effort due to incorporating graph product rules and canonical forms for symmetric and cyclically symmetric structures.

• 정보과학회 컴퓨팅의 실제 논문지
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• 제24권1호
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• pp.40-45
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• 2018

빅데이터와 소셜 네트워크의 발전과 더불어 거대한 그래프를 처리하는 연구도 활발하게 진행되고 있다. 최근 그래프 처리의 성능 향상을 위해 Gorder 라는 그래프 오더링 기법이 제안되었다. 이 기법은 메모리 상의 그래프 레이아웃을 변형하여 데이터 접근 패턴을 CPU 캐시에 적합하게 바꿈으로써 성능을 향상시킨다. 하지만 그래프 알고리즘의 캐시 지역성에만 초점을 두고 설계되었기 때문에 디스크 기반 그래프 엔진에서는 적합하지 않고 전처리 비용도 크다는 문제점이 있다. 제시한 문제점을 해결하기 위해, 본 논문에서는 새로운 그래프 오더링인 I/O Order를 제안하였다. I/O Order는 디스크 기반의 그래프 엔진에서 지역성 외에 입출력 부하를 고려하여 설계되었다. 또한, 오더링 비용을 줄이기 위해 간단한 scheme을 사용한다. 본 논문에서 제시된 I/O Order는 Gorder와 비교해 전처리 비용이 최대 9.6배 감소하였고 성능은 지역성이 낮은 그래프 알고리즘에서 Random 대비 최대 2배 이상 향상되었다.

• 대한수학회보
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• 제33권1호
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• pp.119-126
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• 1996

In this paper we study the asymptotic behavior of the edge independence number of a random (n,n)-tree. The tools we use include the matrix-tree theorem, the probabilistic method and Hall's theorem. We begin with some definitions. An (n,n)_tree T is a connected, acyclic, bipartite graph with n light and n dark vertices (see [Pa92]). A subset M of edges of a graph is called independent(or matching) if no two edges of M are adfacent. A subset S of vertices of a graph is called independent if no two vertices of S are adjacent. The edge independence number of a graph T is the number $\beta_1(T)$ of edges in any largest independent subset of edges of T. Let $\Gamma(n,n)$ denote the set of all (n,n)-tree with n light vertices labeled 1, $\ldots$, n and n dark vertices labeled 1, $\ldots$, n. We give $\Gamma(n,n)$ the uniform probability distribution. Our aim in this paper is to find bounds on $\beta_1$(T) for a random (n,n)-tree T is $\Gamma(n,n)$.

• 한국컴퓨터정보학회논문지
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• 제23권12호
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• pp.57-64
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• 2018

In this paper, a method to measure similarity between two graphs is proposed, which is based on centralities of the graphs. The similarity between two graphs $G_1$ and $G_2$ is defined by the difference of distance($G_1$, $G_{R_1}$) and distance($G_2$, $G_{R_2}$), where $G_{R_1}$ and $G_{R_2}$ are set of random graphs that have the same number of nodes and edges as $G_1$ and $G_2$, respectively. Each distance ($G_*$, $G_{R_*}$) is obtained by comparing centralities of $G_*$ and $G_{R_*}$. Through the computational experiments, we show that it is possible to compare graphs regardless of the number of vertices or edges of the graphs. Also, it is possible to identify and classify the properties of the graphs by measuring and comparing similarities between two graphs.

• 스마트미디어저널
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• 제12권1호
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• pp.9-16
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• 2023

최근 농가의 사과 품질 선별 작업에서 인적자원의 한계를 극복하기 위해 합성곱 신경망(CNN) 기반 시스템이 개발되고 있다. 그러나 합성곱 신경망은 동일한 크기의 이미지만을 입력받기 때문에 샘플링 등의 전처리 과정이 요구될 수 있으며, 과도 샘플링의 경우 화질 저하, 블러링 등 원본 이미지의 정보손실 문제가 발생한다. 본 논문에서는 위 문제를 최소화하기 위하여, 원본 이미지의 패치 기반 그래프를 생성하고 그래프 트랜스포머 모델의 랜덤워크 기반 위치 인코딩 방법을 제안한다. 위 방법은 랜덤워크 알고리즘 기반 위치정보가 없는 패치들의 위치 임베딩 정보를 지속적으로 학습하고, 기존 그래프 트랜스포머의 자가 주의집중 기법을 통해 유익한 노드정보들을 집계함으로써 최적의 그래프 구조를 찾는다. 따라서 무작위 노드 순서의 새로운 그래프 구조와 이미지의 객체 위치에 따른 임의의 그래프 구조에서도 강건한 성질을 가지며, 좋은 성능을 보여준다. 5가지 사과 품질 데이터셋으로 실험하였을 때, 다른 GNN 모델보다 최소 1.3%에서 최대 4.7%의 학습 정확도가 높았으며, ResNet18 모델의 23.52M보다 약 15% 적은 3.59M의 파라미터 수를 보유하여 연산량 절감에 따른 빠른 추론 속도를 보이며 그 효과를 증명한다.

• 한국공간정보시스템학회 논문지
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• 제11권2호
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• pp.13-18
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• 2009

This paper presents the implementation procedure of encoding and decoding algorithms for Tornado code that can provide fault tolerance for storage and transmission system. The degree distribution satisfying heavy tail distribution is produced. Based on this distribution, a good random irregular bipartite graph is attained after plenty of trails. Such graph construction is proved to be efficient, and the experiments also demonstrate that the implementation obtains good performance in terms of decoding overhead.