Graph Spectral Filtering for Network Simplification

Dias, Markus Diego; Petronetto, Fabiano; Valdivia, Paola; Nonato, Luís Gustavo

doi:10.1109/sibgrapi.2018.00051

Cited by 3 publications

(3 citation statements)

References 27 publications

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“…Recently, various research topics related to graph simplification have been proposed in many areas. The summary of related research areas about graph simplification is as follows, i.e., data mining [10], decentralized composite optimization [11], network model simplification [12]- [16], biological network analysis [17], scheduling [18], and clustering coefficient [19]. As such, interest in graph simplification dramatically increases.…”

Section: Introductionmentioning

confidence: 99%

Kirchhoff's Circuit Law Applications to Graph Simplification in Search Problems

Choi

Kim

2020

Preprint

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This paper proposes a new analysis of graph using the concept of electric potential, and also proposes a graph simplification method based on this analysis. Suppose that each node in the weighted-graph has its respective potential value. Furthermore, suppose that the start and terminal nodes in graphs have maximum and zero potentials, respectively. When we let the level of each node be defined as the minimum number of edges/hops from the start node to the node, the proper potential of each level can be estimated based on geometric proportionality relationship. Based on the estimated potential for each level, we can re-design the graph for path-finding problems to be the electrical circuits, thus Kirchhoff's Circuit Law can be directed applicable for simplifying the graph for path-finding problems.• Kirchhoff's Current Law: KCL, also called Kirchhoff's first law, states that the sum of incoming currents at a junction is equal to the sum of outgoing currents at the junction. If we define the sign of incoming currents at the junction as positive and the sign of outgoing currents

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Section: Introductionmentioning

confidence: 99%

Kirchhoff's Circuit Law Applications to Graph Simplification in Search Problems

Choi

Kim

2020

Preprint

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“…• No capítulo 3 descrevemos a técnica HNMF (DIAS et al, 2017) de simplificação de redes com dados multivariados. 25 • No capítulo 4 mostramos um estudo sobre a utilização da teoria de processamento de sinais em grafos como ferramenta de pré-processamento dos dados voltada para a simplificação de uma rede (DIAS et al, 2018).…”

Section: Introductionunclassified

“…Durante o doutorado foram publicados os trabalhos "VizLattes: a Tool for Relevance Analysis from Scientific Co-Authorship Networks" , "A Hierarchical Network Simplification via Non-Negative Matrix Factorization" e "Graph Spectral Filtering for Network Simplification" (DIAS et al, 2018). O segundo recebeu o prêmio de menção honrosa na premiação de melhor trabalho de computação gráfica e visualização na track principal do SIBGRAPI 2017.…”

Section: Introductionunclassified

Simplificação e análise de redes com dados multivariados

Dias¹

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As técnicas de visualização desempenham um papel importante na assistência e compreensão de redes e seus elementos. No entanto, quando enfrentamos redes massivas, a análise tende a ser prejudicada pela confusão visual. Esquemas de simplificação e agrupamento têm sido algumas das principais alternativas neste contexto. No entanto, a maioria das técnicas de simplificação consideram apenas informações extraídas da topologia da rede, desconsiderando conteúdo adicional definido nos nós ou arestas da rede.Neste trabalho, propomos dois estudos. Primeiro uma nova metodologia para simplificação de redes que utiliza tanto a topologia quanto o conteúdo associado aos elementos de rede. A metodologia proposta baseia-se na fatoração de matriz não negativa (NMF) e emparelhamento para realizar a simplificação, combinadas para gerar uma representação hierárquica da rede, agrupando elementos semelhantes em cada nível da hierarquia. Propomos também um estudo da utilização da teoria de processamento de sinal em grafos para filtrar os dados associados aos elementos da rede e o seu efeito no processo de simplificação.Palavras-chave: Redes, Agrupamento, Fatoração de matrizes não negativas, Visualização, Emparelhamento de grafos.ABSTRACT DIAS, M. D. S. S. Simplification and analysis of network with multivariate data. 2018. 81 p. Tese (Doutorado em Ciências -Visualization tools play an important role in assisting and understanding networks and their elements. However, when faced with larger networks, analytical tasks can be hindered by visual clutter. Schemes of simplification and clustering have been a main alternative in this context. Nevertheless, most simplification techniques consider only information extracted from the network topology, disregarding additional content defined in nodes or edges.In this paper, we propose two studies. First, a new methodology for network simplification that uses both topology and content associated with network elements. The proposed methodology is based on non-negative matrix factorization (NMF) and graph matching to perform the simplification, combined to generate a hierarchical representation of the network, grouping the most similar elements at each level of a hierarchy. We also provide a study of the use of the graph signal processing theory to filter data associated to the elements of a network and its effect in the process of simplification.

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Kirchhoff’s Circuit Law Applications to Graph Simplification in Search Problems

Choi

Kim

2020

2020 International Conference on Information and Communication Technology Convergence (ICTC)

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Graph Spectral Filtering for Network Simplification

Cited by 3 publications

References 27 publications

Kirchhoff's Circuit Law Applications to Graph Simplification in Search Problems

Kirchhoff's Circuit Law Applications to Graph Simplification in Search Problems

Simplificação e análise de redes com dados multivariados

Kirchhoff’s Circuit Law Applications to Graph Simplification in Search Problems

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