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.

Windowed Fractional Fourier Transform on Graphs: Fractional Translation Operator and Hausdorff-Young Inequality

Abstract: Designing transform method to identify and exploit structure in signals on weighted graphs is one of the key challenges in the area of signal processing on graphs. So we need to account for the intrinsic geometric structure of the underlying graph data domain. In this paper we generalize the windowed fractional Fourier transform to the graph setting. First we review the windowed fractional Fourier transform and introduce spectral graph theory. Then we define a fractional translation operator with interesting property for signals on graphs. Moreover, we use the operator to define a windowed graph fractional Fourier transform, and explore the reconstruction formula. Finally, the Hausdorff-Young inequality established on this new transform is obtained.

Neumann Cheeger constants on graphs

Abstract: For any subgraph of a graph, the Laplacian with Neumann boundary condition was introduced by Chung and Yau [CY94]. In this paper, motivated by the Riemannian case, we introduce the Cheeger constants for Neumann problems and prove corresponding Cheeger estimates for first nontrivial eigenvalues.

Riemannian Shape Analysis Based on Meridian Curves

Abstract: Comparing different shapes is a fundamental problem in Computational Anatomy (CA), where a rigorous and intrinsic distance metric is key for a shape analysis system to work effectively and consistently. In this paper, we propose a shape comparison and classification framework that consists of two major components. A meridian-based shape representation, stemmed from spectral graph theory, possesses the merit of being able to capture the salient structure property along the direction of maximal shape variations. The meridian extraction algorithm, relying on a discrete approximation of the gradient of the induced Fiedler function, can also be utilized for other purposes, e.g., mesh generation for three-dimensional objects. After projecting the 3D meridians onto a multi-dimensional sphere, similarity/dissimilarity between shapes can be computed based on a Riemannian spherical distance metric. Group statistics, as well as object classification/clustering, can be readily carried out. We demonstrate the effectiveness of our framework with subcortical structures extracted from human brain MR images.

Alarm Association Algorithms Based on Spectral Graph Theory

Abstract: currently those algorithms to mine the alarm association rules are limited to the minimal support, so that they can only obtain the association rules among the frequently occurring alarms. This paper proposes a new mining algorithm based on spectral graph theory. The algorithms firstly sets up alarm association model with time series; Secondly, it regards alarms database as a high-dimensional structure and treats alarms with associated characteristics as part of it. The algorithm discovers the underlying mapping low-dimensional structure embedding in high-dimensional space based on spectral graph theory. Experimental results based on synthetic and real datasets demonstrates that this algorithm not only discoveries association among alarms, but also acquires the fault in the telecommunications network based on the spectral graph transformation.