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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3 citations
TL;DR: A new method is applied to find improved spectral bounds for the well-known Cheeger constant, the Max Cut problem and the expander mixing lemma, and to study cut sizes in the hypercube graph, revealing that a significant improvement over the standard bounds is possible.
3 citations
TL;DR: The main result is Corollary 2.9 which provides upper bounds on, and even better, approximates the largest non-trivial eigenvalue in absolute value of real constant row-sum matrices by the use of v...
Abstract: The main result is Corollary 2.9 which provides upper bounds on, and even better, approximates the largest non-trivial eigenvalue in absolute value of real constant row-sum matrices by the use of v...
3 citations
24 Feb 2013
TL;DR: A general framework for graph adjacency matrices and any rectangular binary matrix, and a randomization test for fixing K* of the relevant eigenspace of a general binary datatable is proposed.
Abstract: Laplacian low-rank approximations are much appreciated in the context of graph spectral methods and Correspondence Analysis. We address here the problem of determining the dimensionality K* of the relevant eigenspace of a general binary datatable by a statistically well-founded method. We propose 1) a general framework for graph adjacency matrices and any rectangular binary matrix, 2) a randomization test for fixing K*. We illustrate with both artificial and real data.
3 citations
Posted Content•
TL;DR: An anisotropic, directed diffusion operator corresponding to flow on a directed graph, from a directed affinity matrix developed with coherence in mind, and corresponding spectral graph theory from the graph Laplacian is developed.
Abstract: Viewing a data set such as the clouds of Jupiter, coherence is readily apparent to human observers, especially the Great Red Spot, but also other great storms and persistent structures. There are now many different definitions and perspectives mathematically describing coherent structures, but we will take an image processing perspective here. We describe an image processing perspective inference of coherent sets from a fluidic system directly from image data, without attempting to first model underlying flow fields, related to a concept in image processing called motion tracking. In contrast to standard spectral methods for image processing which are generally related to a symmetric affinity matrix, leading to standard spectral graph theory, we need a not symmetric affinity which arises naturally from the underlying arrow of time. We develop an anisotropic, directed diffusion operator corresponding to flow on a directed graph, from a directed affinity matrix developed with coherence in mind, and corresponding spectral graph theory from the graph Laplacian. Our examples will include partitioning the weather and cloud structures of Jupiter, and a local to Potsdam, N.Y. lake-effect snow event on Earth, as well as the the benchmark test double-gyre system.
3 citations