Topic
Spectral graph theory
About: Spectral graph theory is a research topic. Over the lifetime, 1334 publications have been published within this topic receiving 77373 citations.
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27 Jun 2004
TL;DR: A method for clustering and embedding WWW images by using a vision-based page segmentation algorithm, and the textual and link information of an image can be accurately extracted from the block containing that image.
Abstract: Due to the rapid growth of the number of digital images on the Web, there is an increasing demand for an effective and efficient method of organizing and retrieving the images available. This paper describes a method for clustering and embedding WWW images. By using a vision-based page segmentation algorithm, a Web page is partitioned into blocks, and the textual and link information of an image can be accurately extracted from the block containing that image. By extracting the page-to-block, block-to-image, block-to-page relationships through a link structure and page layout analysis, we construct an image graph. With the image graph model, we use techniques from spectral graph theory for image clustering and embedding. Some experimental results are given in the paper.
51 citations
Journal Article•
TL;DR: The clustering principle based on graph theory is first introduced, and then spectral clustering algorithms are categorized according to rules of graph partition, and typical algorithms are studied emphatically.
Abstract: Spectral clustering algorithms are newly developing technique in recent yearsUnlike the traditional clustering algorithms,these apply spectral graph theory to solve the clustering of non-convex sphere of sample spaces,so that they can be converged to global optimal solutionIn this paper,the clustering principle based on graph theory is first introduced,and then spectral clustering algorithms are categorized according to rules of graph partition,and typical algorithms are studied emphatically,as well as their advantages and disadvantages are presented in detailFinally,some valuable directions for further research are proposed
50 citations
TL;DR: A novel, computationally efficient, approach to graph clustering in the evolutionary context called Incremental Approximate Spectral Clustering (IASC) is introduced and a theoretical bound on the quality of the approximate eigenvectors using perturbation theory is presented.
49 citations
TL;DR: This spectral graph model demonstrates that certain brain oscillations are emergent properties of the graph structure of the structural connectome and provides important insights towards understanding the fundamental relationship between network topology and macroscopic whole‐brain dynamics.
Abstract: The relationship between the brain's structural wiring and the functional patterns of neural activity is of fundamental interest in computational neuroscience. We examine a hierarchical, linear graph spectral model of brain activity at mesoscopic and macroscopic scales. The model formulation yields an elegant closed-form solution for the structure-function problem, specified by the graph spectrum of the structural connectome's Laplacian, with simple, universal rules of dynamics specified by a minimal set of global parameters. The resulting parsimonious and analytical solution stands in contrast to complex numerical simulations of high dimensional coupled nonlinear neural field models. This spectral graph model accurately predicts spatial and spectral features of neural oscillatory activity across the brain and was successful in simultaneously reproducing empirically observed spatial and spectral patterns of alpha-band (8-12 Hz) and beta-band (15-30 Hz) activity estimated from source localized magnetoencephalography (MEG). This spectral graph model demonstrates that certain brain oscillations are emergent properties of the graph structure of the structural connectome and provides important insights towards understanding the fundamental relationship between network topology and macroscopic whole-brain dynamics. .
49 citations
TL;DR: In this article, a general method for obtaining a vacuum spectral distribution of the adjacency matrix of a star graph is established within the framework of quantum probability theory, and the spectral distribution tends asymptotically to the Bernoulli distribution.
Abstract: A general method for obtaining a vacuum spectral distribution of the adjacency matrix of a star graph is established within the framework of quantum probability theory. The spectral distribution tends asymptotically to the Bernoulli distribution as the number of leaves of a star graph tends to the infinity.
49 citations