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
More filters
Posted Content•
TL;DR: GraphFlow as mentioned in this paper decomposes a graph into families of non-intersecting one dimensional (1D) paths, after which, a 1D CNN is applied along each family of paths.
Abstract: In view of the huge success of convolution neural networks (CNN) for image classification and object recognition, there have been attempts to generalize the method to general graph-structured data. One major direction is based on spectral graph theory and graph signal processing. In this paper, we study the problem from a completely different perspective, by introducing parallel flow decomposition of graphs. The essential idea is to decompose a graph into families of non-intersecting one dimensional (1D) paths, after which, we may apply a 1D CNN along each family of paths. We demonstrate that the our method, which we call GraphFlow, is able to transfer CNN architectures to general graphs. To show the effectiveness of our approach, we test our method on the classical MNIST dataset, synthetic datasets on network information propagation and a news article classification dataset.
3 citations
TL;DR: This paper describes the use of Riemannian geometry, and in particular the relationship between the Laplace-Beltrami operator and the graph Laplacian, for the purposes of embedding a graph onto a Riem Mannian manifold.
Abstract: In this paper, we describe the use of Riemannian geometry, and in particular the relationship between the Laplace-Beltrami operator and the graph Laplacian, for the purposes of embedding a graph onto a Riemannian manifold. Using the properties of Jacobi fields, we show how to compute an edge-weight matrix in which the elements reflect the sectional curvatures associated with the geodesic paths between nodes on the manifold. We use the resulting edge-weight matrix to embed the nodes of the graph onto a Riemannian manifold of constant sectional curvature. With the set of embedding coordinates at hand, the graph matching problem is cast as that of aligning pairs of manifolds subject to a geometric transformation. We illustrate the utility of the method on image matching using the COIL database.
3 citations
TL;DR: In this article, a general class of recurrence relations appeared in the application of matrix diagonalization procedure and they were studied in several problems involving eigenvalues of graphs, and the results of these relations were applied to several graph problems.
Abstract: We study a general class of recurrence relations that appear in the application of a matrix diagonalization procedure. We find general closed formula and determine analytical properties of the solutions. We finally apply these findings in several problems involving eigenvalues of graphs.
3 citations
TL;DR: In this paper, the authors extend spectral graph theory from integral circulant graphs with prime power order to a Cayley graph over a finite chain ring and determine the spectrum and energy of such graphs.
Abstract: We extend spectral graph theory from the integral circulant graphs with prime power order to a Cayley graph over a finite chain ring and determine the spectrum and energy of such graphs. Moreover, we apply the results to obtain the energy of some gcd-graphs on a quotient ring of a unique factorisation domain.
3 citations
Patent•
23 Jul 2013TL;DR: In this article, a graph Laplacian is determined from the graph from the prior information, and a graph spectral constraint is derived from the spectral constraint to identify a segment of target points in the data.
Abstract: A method segments n-dimensional by first determining prior information from the data. A fidelity term is determined from the prior information, and the data are represented as a graph. A graph Laplacian is determined from the graph from the graph, and a Laplacian spectrum constraint is determined from the graph Laplacian. Then, an objective function is minimized according to the fidelity term and the Laplacian spectrum constraint to identify a segment of target points in the data.
3 citations