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CuninghameGreen: Reducible spectral theory with applications to the robustness of matrices in maxalgebra, The University of Birmingham, preprint 2007/16
"... Abstract. Let a ⊕ b = max(a, b) and a ⊗ b = a + b for a, b ∈ R: = R ∪ {−∞}. By maxalgebra we understand the analogue of linear algebra developed for the pair of operations (⊕,⊗), extended to matrices and vectors. The symbol Ak stands for the kth maxalgebraic power of a square matrix A. Let us deno ..."
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Cited by 10 (3 self)
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×n, is there a k such that Ak ⊗ x is a maxalgebraic eigenvector of A? If the answer is affirmative for every x = ε, then A is called robust. First, we give a complete account of the reducible maxalgebraic spectral theory, and then we apply it to characterize robust matrices.
Finding community structure in networks using the eigenvectors of matrices
, 2006
"... We consider the problem of detecting communities or modules in networks, groups of vertices with a higherthanaverage density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as “modularity ” over possible div ..."
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Cited by 500 (0 self)
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We consider the problem of detecting communities or modules in networks, groups of vertices with a higherthanaverage density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as “modularity ” over possible
Detection of Abrupt Changes: Theory and Application
 HTTP://PEOPLE.IRISA.FR/MICHELE.BASSEVILLE/KNIGA/
, 1993
"... ..."
On Spectral Clustering: Analysis and an algorithm
 ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS
, 2001
"... Despite many empirical successes of spectral clustering methods  algorithms that cluster points using eigenvectors of matrices derived from the distances between the points  there are several unresolved issues. First, there is a wide variety of algorithms that use the eigenvectors in slightly ..."
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Cited by 1697 (13 self)
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Despite many empirical successes of spectral clustering methods  algorithms that cluster points using eigenvectors of matrices derived from the distances between the points  there are several unresolved issues. First, there is a wide variety of algorithms that use the eigenvectors
Domain Theory
 Handbook of Logic in Computer Science
, 1994
"... Least fixpoints as meanings of recursive definitions. ..."
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Cited by 546 (25 self)
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Least fixpoints as meanings of recursive definitions.
Stochastic Perturbation Theory
, 1988
"... . In this paper classical matrix perturbation theory is approached from a probabilistic point of view. The perturbed quantity is approximated by a firstorder perturbation expansion, in which the perturbation is assumed to be random. This permits the computation of statistics estimating the variatio ..."
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Cited by 886 (35 self)
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. In this paper classical matrix perturbation theory is approached from a probabilistic point of view. The perturbed quantity is approximated by a firstorder perturbation expansion, in which the perturbation is assumed to be random. This permits the computation of statistics estimating
Results 1  10
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