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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TL;DR: A general anonymity model against weight-related attacks, and a new utility metric based on spectral graph theory is introduced, which is effective in terms of efficiency and data utility preservation.
7 citations
Journal Article•
7 citations
TL;DR: It is demonstrated how the addition of edges increases the trace of the steady-state value of the position error covariance matrix, and the theoretical predictions are verified through simulation analysis.
Abstract: A group of mobile robots can localize cooperatively, using relative position and absolute orientation measurements, fused through an extended Kalman filter (ekf). The topology of the graph of relative measurements is known to affect the steady-state value of the position error covariance matrix. Classes of sensor graphs are identified, for which tight bounds for the trace of the covariance matrix can be obtained based on the algebraic properties of the underlying relative measurement graph. The string and the star graph topologies are considered, and the explicit form of the eigenvalues of error covariance matrix is given. More general sensor graph topologies are considered as combinations of the string and star topologies, when additional edges are added. It is demonstrated how the addition of edges increases the trace of the steady-state value of the position error covariance matrix, and the theoretical predictions are verified through simulation analysis.
7 citations
TL;DR: In this article, the evolving set methodology is used to show Cheeger inequalities for bounding the spectral gap of a finite Markov kernel, including edge-expansion, vertexexpansion and mixtures of both.
Abstract: We show how the evolving set methodology of Morris and Peres can be used to show Cheeger inequalities for bounding the spectral gap of a finite Markov kernel. This leads to sharp versions of several previous Cheeger inequalities, including ones involving edge-expansion, vertex-expansion, and mixtures of both. A bound on the smallest eigenvalue also follows.
7 citations
24 Aug 2014
TL;DR: A new multiplicative update rule for the optimization task is proposed in terms of a particular factorization of the adjacency matrix of the original graph in a way to minimize reconstruction error.
Abstract: We address the problem of encoding a graph of order n into a graph of order k n in a way to minimize reconstruction error. We characterize this encoding in terms of a particular factorization of the adjacency matrix of the original graph. The factorization is determined as the solution of a discrete optimization problem, which is for convenience relaxed into a continuous, but equivalent, one. We propose a new multiplicative update rule for the optimization task. Experiments are conducted to assess the effectiveness of the proposed approach.
7 citations