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Eigenvalue and Eigenvector Analysis of Dynamic Systems
"... While several methods aimed at understanding the causes of model behavior have been proposed in recent years, formal model analysis remains an important and challenging area in system dynamics. This paper describes a mathematical method to incorporate eigenvectors to the more traditional eigenvalue ..."
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Cited by 2 (0 self)
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While several methods aimed at understanding the causes of model behavior have been proposed in recent years, formal model analysis remains an important and challenging area in system dynamics. This paper describes a mathematical method to incorporate eigenvectors to the more traditional eigenvalue
Quantum searching, counting and amplitude amplification by eigenvector analysis
 IN PROCEEDINGS OF RANDOMIZED ALGORITHMS, WORKSHOP OF MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE
, 1998
"... Grovers quantum searching algorithm uses a quantum computer to find the solution to fx for a given function f The algorithm which repeatedly applies a certain operator G has led to a major family of quantum algorithms for generating and counting solutions to fx for more general f By st ..."
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Cited by 18 (1 self)
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By studying the eigenvectors and eigenvalues of G and its variations we arrive at simple algorithms and analyses for quantum searching approximate counting and amplitude amplication and estimation
Quantum Searching, Counting and Amplitude Amplification by Eigenvector Analysis
 In MFCS'98 Workshop on Randomized Algorithms
, 1998
"... Grover's quantum searching algorithm uses a quantum computer to find the solution to f(x) = 1 for a given function f . The algorithm, which repeatedly applies a certain operator G, has led to a major family of quantum algorithms for generating and counting solutions to f(x) = 1 for more general ..."
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general f . By studying the eigenvectors and eigenvalues of G and its variations, we arrive at simple algorithms and analyses for quantum searching, approximate counting, and amplitude amplification and estimation. 1 Introduction Grover's original quantum searching algorithm [7] showed that we
Segmentation using eigenvectors: A unifying view
 In ICCV
, 1999
"... Automatic grouping and segmentation of images remains a challenging problem in computer vision. Recently, a number of authors have demonstrated good performance on this task using methods that are based on eigenvectors of the a nity matrix. These approaches are extremely attractive in that they are ..."
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Cited by 380 (1 self)
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highlighting their distinguishing features. We then prove results on eigenvectors of block matrices that allow us to analyze the performance of these algorithms in simple grouping settings. Finally, we use our analysis to motivate a variation on the existing methods that combines aspects from di erent
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 1713 (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
Canonical correspondence analysis: a new eigenvector technique for multivariate direct gradient analysis.
, 1986
"... ..."
Consistency of spectral clustering
, 2004
"... Consistency is a key property of statistical algorithms, when the data is drawn from some underlying probability distribution. Surprisingly, despite decades of work, little is known about consistency of most clustering algorithms. In this paper we investigate consistency of a popular family of spe ..."
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Cited by 572 (15 self)
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of spectral clustering algorithms, which cluster the data with the help of eigenvectors of graph Laplacian matrices. We show that one of the two of major classes of spectral clustering (normalized clustering) converges under some very general conditions, while the other (unnormalized), is only consistent
Grounding in communication
 In
, 1991
"... We give a general analysis of a class of pairs of positive selfadjoint operators A and B for which A + XB has a limit (in strong resolvent sense) as h10 which is an operator A, # A! Recently, Klauder [4] has discussed the following example: Let A be the operator(d2/A2) + x2 on L2(R, dx) and let ..."
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Cited by 1122 (20 self)
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We give a general analysis of a class of pairs of positive selfadjoint operators A and B for which A + XB has a limit (in strong resolvent sense) as h10 which is an operator A, # A! Recently, Klauder [4] has discussed the following example: Let A be the operator(d2/A2) + x2 on L2(R, dx) and let
Authoritative Sources in a Hyperlinked Environment
 JOURNAL OF THE ACM
, 1999
"... The network structure of a hyperlinked environment can be a rich source of information about the content of the environment, provided we have effective means for understanding it. We develop a set of algorithmic tools for extracting information from the link structures of such environments, and repo ..."
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Cited by 3632 (12 self)
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an algorithmic formulation of the notion of authority, based on the relationship between a set of relevant authoritative pages and the set of “hub pages ” that join them together in the link structure. Our formulation has connections to the eigenvectors of certain matrices associated with the link graph
Eigenvector Analysis of Digital Elevation Models in a GIS: Geomorphometry and Quality Control
"... Abstract. Digital elevation models (DEMs) cover a wide range of scales, and allow statisticalanalysis of geomorphometric parameters. At global or continental scale, DEMs covering rectangular quadrangles can be considered random samples. Average quadrangle values can be compared at different DEM scal ..."
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variables computed from 10 m and 30 m USGS Level 2 DEMs are essentially identical. Slope algorithms perform differently in different physiographic provinces, and the aspect algorithm performs poorly in low relief areas. Geomorphometric analysis can provide a rapid and effective assessment of DEM quality
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