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1,335
Laplacian eigenmaps and spectral techniques for embedding and clustering.
 Proceeding of Neural Information Processing Systems,
, 2001
"... Abstract Drawing on the correspondence between the graph Laplacian, the LaplaceBeltrami op erator on a manifold , and the connections to the heat equation , we propose a geometrically motivated algorithm for constructing a representation for data sampled from a low dimensional manifold embedded in ..."
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Cited by 668 (7 self)
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of the manifold on which the data may possibly reside. Recently, there has been some interest (Tenenbaum et aI, 2000 ; The core algorithm is very simple, has a few local computations and one sparse eigenvalu e problem. The solution reflects th e intrinsic geom etric structure of the manifold. Th e justification
Testing for Common Trends
 Journal of the American Statistical Association
, 1988
"... Cointegrated multiple time series share at least one common trend. Two tests are developed for the number of common stochastic trends (i.e., for the order of cointegration) in a multiple time series with and without drift. Both tests involve the roots of the ordinary least squares coefficient matrix ..."
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Cited by 464 (7 self)
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similar. The firstest (qf) is developed under the assumption that certain components of the process have a finiteorder vector autoregressive (VAR) representation, and the nuisance parameters are handled by estimating this VAR. The second test (q,) entails computing the eigenvalues of a corrected sample
The eigenvalues of random symmetric matrices
 Combinatorica
, 1981
"... Let A:(at;) be an zxn matrix whose entries for i=j are independent random variables and ai;:aii. Suppose that every a;; is bounded and for eveÍy i>j we have Eaii:!, D2ai,:62 and Eaiiv. E. P. Wigner determined the asymptotic behavior of the eigenvalues of I (semicircle law). In particular, for a ..."
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Cited by 179 (0 self)
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,,(x):: (number of eigenvalues =x)ln' One is interested in the limiting behavior of the sequence W,, of random distribution functions as n*@.
Region Covariance: A Fast Descriptor for Detection And Classification
 In Proc. 9th European Conf. on Computer Vision
, 2006
"... We describe a new region descriptor and apply it to two problems, object detection and texture classification. The covariance of dfeatures, e.g., the threedimensional color vector, the norm of first and second derivatives of intensity with respect to x and y, etc., characterizes a region of in ..."
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Cited by 278 (14 self)
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of interest. We describe a fast method for computation of covariances based on integral images. The idea presented here is more general than the image sums or histograms, which were already published before, and with a series of integral images the covariances are obtained by a few arithmetic operations
On the Rank of Extreme Matrices in Semidefinite Programs and the Multiplicity of Optimal Eigenvalues
, 1998
"... We derive some basic results on the geometry of semidefinite programming (SDP) and eigenvalueoptimization, i.e., the minimization of the sum of the k largest eigenvalues of a smooth matrixvalued function. We provide upper bounds on the rank of extreme matrices in SDPs, and the first theoretically ..."
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Cited by 111 (1 self)
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solid explanation of a phenomenon of intrinsic interest in eigenvalueoptimization. In the spectrum of an optimal matrix, the kth and (k / 1)st largest eigenvalues tend to be equal and frequently have multiplicity greater than two. This clustering is intuitively plausible and has been observed as early
Convex optimization of graph Laplacian eigenvalues
 IN INTERNATIONAL CONGRESS OF MATHEMATICIANS
"... We consider the problem of choosing the edge weights of an undirected graph so as to maximize or minimize some function of the eigenvalues of the associated Laplacian matrix, subject to some constraints on the weights, such as nonnegativity, or a given total value. In many interesting cases this p ..."
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Cited by 51 (0 self)
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We consider the problem of choosing the edge weights of an undirected graph so as to maximize or minimize some function of the eigenvalues of the associated Laplacian matrix, subject to some constraints on the weights, such as nonnegativity, or a given total value. In many interesting cases
Spectra of random graphs with given expected degrees
, 2003
"... In the study of the spectra of power law graphs, there are basically two competing approaches. One is to prove analogues of Wigner’s semicircle law while the other predicts that the eigenvalues follow a power law distributions. Although the semicircle law and the power law have nothing in common, ..."
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Cited by 180 (19 self)
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power law graph obeys the power law. Our results are based on the analysis of random graphs with given expected degrees and their relations to several key invariants. Of interest are a number of (new) values for the exponent β where phase transitions for eigenvalue distributions occur. The spectrum
The structure of complete stable minimal surfaces in 3manifolds of nonnegative scalar curvature.
 Comm. Pure Appli. Math.
, 1980
"... The purpose of this paper is to study minimal surfaces in threedimensional manifolds which, on each compact set, minimize area up to second order. If M is a minimal surface in a Riemannian threemanifold N, then the condition that M be stable is expressed analytically by the requirement that o n a ..."
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Cited by 192 (1 self)
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any compact domain of M, the first eigenvalue of the operator A+Ric(v)+(AI* be positive. Here Ric (v) is the Ricci curvature of N in the normal direction to M and (A)' is the square of the length of the second fundamental form of M. In the case that N is the flat R3, we prove that any complcte
Quaternionic eigenvalue problem
 J. Math. Physics
"... We discuss the ͑right͒ eigenvalue equation for H, C and R linear quaternionic operators. The possibility to introduce an isomorphism between these operators and real/complex matrices allows us to translate the quaternionic problem into an equivalent real or complex counterpart. Interesting applicat ..."
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Cited by 8 (7 self)
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We discuss the ͑right͒ eigenvalue equation for H, C and R linear quaternionic operators. The possibility to introduce an isomorphism between these operators and real/complex matrices allows us to translate the quaternionic problem into an equivalent real or complex counterpart. Interesting
Regularized Gaussian Discriminant Analysis Through Eigenvalue Decomposition
 Journal of the American Statistical Association
, 1996
"... Friedman (1989) has proposed a regularization technique (RDA) of discriminant analysis in the Gaussian framework. RDA makes use of two regularization parameters to design an intermediate classi cation rule between linear and quadratic discriminant analysis. In this paper, we propose an alternative a ..."
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Cited by 54 (7 self)
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approach to design classi cation rules which have also a median position between linear and quadratic discriminant analysis. Our approach is based on the reparametrization of the covariance matrix k of a group Gk in terms of its eigenvalue decomposition, k = kDkAkD 0 k where k speci es the volume of Gk, Ak
Results 1  10
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1,335