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Spectral methods for graph clustering - A survey

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  • Nascimento, Mariá C.V.
  • de Carvalho, André C.P.L.F.

Abstract

Graph clustering is an area in cluster analysis that looks for groups of related vertices in a graph. Due to its large applicability, several graph clustering algorithms have been proposed in the last years. A particular class of graph clustering algorithms is known as spectral clustering algorithms. These algorithms are mostly based on the eigen-decomposition of Laplacian matrices of either weighted or unweighted graphs. This survey presents different graph clustering formulations, most of which based on graph cut and partitioning problems, and describes the main spectral clustering algorithms found in literature that solve these problems.

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  • Nascimento, Mariá C.V. & de Carvalho, André C.P.L.F., 2011. "Spectral methods for graph clustering - A survey," European Journal of Operational Research, Elsevier, vol. 211(2), pages 221-231, June.
    • Handle: RePEc:eee:ejores:v:211:y:2011:i:2:p:221-231
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    1. Pablo M. Gleiser & Leon Danon, 2003. "Community Structure In Jazz," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 6(04), pages 565-573.
    2. Kenneth M. Hall, 1970. "An r-Dimensional Quadratic Placement Algorithm," Management Science, INFORMS, vol. 17(3), pages 219-229, November.
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    2. D’Ambra, Pasqua & Vassilevski, Panayot S. & Cutillo, Luisa, 2023. "Extending bootstrap AMG for clustering of attributed graphs," Applied Mathematics and Computation, Elsevier, vol. 447(C).
    3. Chen, Claire Y.T. & Sun, Edward W. & Miao, Wanyu & Lin, Yi-Bing, 2024. "Reconciling business analytics with graphically initialized subspace clustering for optimal nonlinear pricing," European Journal of Operational Research, Elsevier, vol. 312(3), pages 1086-1107.
    4. Carrizosa, Emilio & Mladenović, Nenad & Todosijević, Raca, 2013. "Variable neighborhood search for minimum sum-of-squares clustering on networks," European Journal of Operational Research, Elsevier, vol. 230(2), pages 356-363.

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