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Nonlinear component analysis as a kernel eigenvalue problem

, 1996
"... We describe a new method for performing a nonlinear form of Principal Component Analysis. By the use of integral operator kernel functions, we can efficiently compute principal components in highdimensional feature spaces, related to input space by some nonlinear map; for instance the space of all ..."
Abstract

Cited by 1554 (85 self)
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We describe a new method for performing a nonlinear form of Principal Component Analysis. By the use of integral operator kernel functions, we can efficiently compute principal components in highdimensional feature spaces, related to input space by some nonlinear map; for instance the space of all possible 5pixel products in 16x16 images. We give the derivation of the method, along with a discussion of other techniques which can be made nonlinear with the kernel approach; and present first experimental results on nonlinear feature extraction for pattern recognition.
The Quadratic Eigenvalue Problem
, 2001
"... . We survey the quadratic eigenvalue problem, treating its many applications, its mathematical properties, and a variety of numerical solution techniques. Emphasis is given to exploiting both the structure of the matrices in the problem (dense, sparse, real, complex, Hermitian, skewHermitian) and t ..."
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Cited by 262 (21 self)
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. We survey the quadratic eigenvalue problem, treating its many applications, its mathematical properties, and a variety of numerical solution techniques. Emphasis is given to exploiting both the structure of the matrices in the problem (dense, sparse, real, complex, Hermitian, skew
An iterative method for the solution of the eigenvalue problem of linear differential and integral
, 1950
"... The present investigation designs a systematic method for finding the latent roots and the principal axes of a matrix, without reducing the order of the matrix. It is characterized by a wide field of applicability and great accuracy, since the accumulation of rounding errors is avoided, through the ..."
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Cited by 525 (0 self)
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the process of "minimized iterations". Moreover, the method leads to a well convergent successive approximation procedure by which the solution of integral equations of the Fredholm type and the solution of the eigenvalue problem of linear differential and integral operators may be accomplished. I.
eigenvalue problems
, 2008
"... We introduce quadratic twoparameter eigenvalue problem and show that we can linearize it as a singular twoparameter eigenvalue problem. This problem, together with another example that comes from model updating, shows the need for numerical methods for singular twoparameter eigenvalue problems an ..."
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We introduce quadratic twoparameter eigenvalue problem and show that we can linearize it as a singular twoparameter eigenvalue problem. This problem, together with another example that comes from model updating, shows the need for numerical methods for singular twoparameter eigenvalue problems
EIGENVALUE PROBLEM
"... Abstract. This paper is concerned with the Hermitian positive definite generalized eigenvalue problem A − λB for partitioned matrices ..."
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Abstract. This paper is concerned with the Hermitian positive definite generalized eigenvalue problem A − λB for partitioned matrices
eigenvalue problem
, 2010
"... The method called Arnoldi is currently a very popular method to solve largescale eigenvalue problems. The general purpose of this paper is to generalize Arnoldi to the characteristic equation of a delaydifferential equation (DDE), here called a delay eigenvalue problem. The DDE can equivalently be ..."
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The method called Arnoldi is currently a very popular method to solve largescale eigenvalue problems. The general purpose of this paper is to generalize Arnoldi to the characteristic equation of a delaydifferential equation (DDE), here called a delay eigenvalue problem. The DDE can equivalently
Eigenvalue Problems
, 2013
"... We present a ChebyshevDavidson method to compute a few smallest positive eigenvalues and corresponding eigenvectors of the linear response eigenvalue problem. The method is actually applicable to the slightly more general linear response eigenvalue problem where purely imaginary eigenvalues may occ ..."
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We present a ChebyshevDavidson method to compute a few smallest positive eigenvalues and corresponding eigenvectors of the linear response eigenvalue problem. The method is actually applicable to the slightly more general linear response eigenvalue problem where purely imaginary eigenvalues may
EIGENVALUE PROBLEMS ∗
"... Abstract. We discuss iterative methods for computing criticality in nuclear reactors. In general this requires the solution of a generalised eigenvalue problem for an unsymmetric integrodifferential operator in 6 independent variables, modelling transport, scattering and fission, where the dependen ..."
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Abstract. We discuss iterative methods for computing criticality in nuclear reactors. In general this requires the solution of a generalised eigenvalue problem for an unsymmetric integrodifferential operator in 6 independent variables, modelling transport, scattering and fission, where
EIGENVALUE PROBLEMS
, 2001
"... The calculation of a few interior eigenvalues of a matrix has not received much attention in the past, most methods being some spinoff of either the complete eigenvalue calculation or a subspace method designed for the extremal part of the spectrum. The reason for this could be the rather chaotic b ..."
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The calculation of a few interior eigenvalues of a matrix has not received much attention in the past, most methods being some spinoff of either the complete eigenvalue calculation or a subspace method designed for the extremal part of the spectrum. The reason for this could be the rather chaotic
Results 1  10
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313,309