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Downsampling graphs using spectral theory
2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2011In this paper we present methods for downsampling datasets defined on graphs (i.e., graph-signals) by extending downsampling results for traditional N-dimensional signals. In particular, we study the spectral properties of k-regular bipartite graphs (K-RBG) and prove that downsampling in these graphs is governed by a Nyquist-like criteria.
Sunil K. Narang, Antonio Ortega
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Survey of spectral clustering based on graph theory
Pattern RecognitionShifei Ding, Di Jin
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2015
The concept of the line graph of a given graph is so natural that it has been independently discovered by many authors. Of course, each author gave it a different name: It was called the interchange graph by Ore [272], derivative by H. Sachs [297], derived graph by L. W. Beineke [52], edge-to-vertex dual by M.
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The concept of the line graph of a given graph is so natural that it has been independently discovered by many authors. Of course, each author gave it a different name: It was called the interchange graph by Ore [272], derivative by H. Sachs [297], derived graph by L. W. Beineke [52], edge-to-vertex dual by M.
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Domination and Spectral Graph Theory
2020Spectral graph theory studies graphs through the eigenvalues and eigenvectors of matrices associated with them. In this chapter we show how domination parameters have appeared in spectral graph theory, including the domination number γ, the total domination number γt, and the signed domination number γs.
Carlos Hoppen +2 more
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Spectral Graph Theory And Eigen Values Of Graphs
Advances in Nonlinear Variational Inequalities, 2023Spectral Graph Theory is a profound interdisciplinary field that bridges linear algebra, combinatorics, and computer science by studying graphs through the spectra (eigenvalues and eigenvectors) of matrices associated with them, such as the adjacency matrix, Laplacian matrix, and normalized Laplacian.
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Graph Structure Similarity using Spectral Graph Theory
2016In understanding an unknown network we search for metrics to determine how close an inferred network that is being analyzed, is to the truth. We develop a metric to test for similarity between an inferred network and the true network. Our method uses the eigenvalues of the adjacency matrix and of the Laplacian at each step of the network discovery to ...
Brian Crawford +4 more
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Characterising insomnia: A graph spectral theory approach
2015 37th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), 2015This paper introduces a computational approach to characterise healthy controls and insomniacs based on graph spectral theory. Based upon expert-generated hypnograms of sleep onset periods, a network of sleep stages transitions is derived to compute four similarity distances amongst subjects' sleeping patterns.
Ramiro Chaparro-Vargas +3 more
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On spectral graph theory in power system restoration
2011 2nd IEEE PES International Conference and Exhibition on Innovative Smart Grid Technologies, 2011A large penetration of renewable energy sources with volatile power generation imposes new challenges for efficient restoration of the power system after a blackout. Prolonged power outages are also characterized be uncertain load conditions due to cold load phenomena.
Fredrik Edström, Lennard Söder
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Spectral graph theory and deep learning on graphs
2017A significant challenge in machine learning problems is learning meaningful repre- sentations that encode all the information that is relevant to a given task. Neural networks focus on learning parameters based on the ability to successfully represent individual samples of a dataset.
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