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.
Papers published on a yearly basis
Papers
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17 Jun 2006
TL;DR: A graph-based approach to classification with only one labeled example per class, based on a robust path-based similarity measure proposed recently, is proposed, which can successfully solve some difficult classification tasks with only very few labeled examples.
Abstract: Classification with only one labeled example per class is a challenging problem in machine learning and pattern recognition. While there have been some attempts to address this problem in the context of specific applications, very little work has been done so far on the problem under more general object classification settings. In this paper, we propose a graph-based approach to the problem. Based on a robust path-based similarity measure proposed recently, we construct a weighted graph using the robust path-based similarities as edge weights. A kernel matrix, called graph Laplacian kernel, is then defined based on the graph Laplacian. With the kernel matrix, in principle any kernel-based classifier can be used for classification. In particular, we demonstrate the use of a kernel nearest neighbor classifier on some synthetic data and real-world image sets, showing that our method can successfully solve some difficult classification tasks with only very few labeled examples.
14 citations
TL;DR: In this article, lower and upper estimates for the spectral gap of the Laplace operator on a finite compact connected metric graph are discussed, and it is shown that the best lower estimate is given by the interval with the same total length as the original graph.
Abstract: We discuss lower and upper estimates for the spectral gap of the Laplace operator on a finite compact connected metric graph. It is shown that the best lower estimate is given by the spectral gap for the interval with the same total length as the original graph. An explicit upper estimate is given by generalizing Cheeger's approach developed originally for Riemannian manifolds.
14 citations
Posted Content•
TL;DR: In this article, the physical Laplacian and the corresponding heat flow on an infinite, locally finite graph with possibly unbounded valence were studied and the authors showed that the heat flow can be represented as a convex convex graph.
Abstract: We study the physical Laplacian and the corresponding heat flow on an infinite, locally finite graph with possibly unbounded valence.
14 citations
TL;DR: In this paper, an embedding of closed Riemannian manifolds into l 2 based on the heat kernel of the Connection Laplacian associated with the Levi-Civita connection on the tangent bundle is introduced.
14 citations
TL;DR: The construction of spectral filters for graph wavelet transforms is addressed and it will be shown how the classical quadrature-mirror-filters and linear phase, critically/over- sampled filter banks can be used to construct spectral graph wavelets that are almost tight.
Abstract: The construction of spectral filters for graph wavelet transforms is addressed in this paper. Both the undecimated and decimated cases will be considered. The filter functions are polynomials and can be implemented efficiently without the need for any eigendecomposition, which is computationally expensive for large graphs. Polynomial filters also have the advantage of the vertex localization property. The construction is achieved by designing suitable transformations that are used on traditional multirate filter banks. It will be shown how the classical quadrature-mirror-filters and linear phase, critically/over- sampled filter banks can be used to construct spectral graph wavelets that are almost tight. A variety of design examples will be given to show the versatility of the design technique.
14 citations