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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 ..."
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Cited by 1573 (83 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
LETTER Communicated by Peter Dayan Nonlinear Component Analysis as a Kernel Eigenvalue Problem
"... A new method for performing a nonlinear form of principal component analysis is proposed. By the use of integral operator kernel functions, one can efficiently compute principal components in highdimensional feature spaces, related to input space by some nonlinear map—for instance, the space of al ..."
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A new method for performing a nonlinear form of principal component analysis is proposed. By the use of integral operator kernel functions, one can efficiently compute principal components in highdimensional feature spaces, related to input space by some nonlinear map—for instance, the space
Convolution Kernels on Discrete Structures
, 1999
"... We introduce a new method of constructing kernels on sets whose elements are discrete structures like strings, trees and graphs. The method can be applied iteratively to build a kernel on an infinite set from kernels involving generators of the set. The family of kernels generated generalizes the fa ..."
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Cited by 506 (0 self)
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the family of radial basis kernels. It can also be used to define kernels in the form of joint Gibbs probability distributions. Kernels can be built from hidden Markov random elds, generalized regular expressions, pairHMMs, or ANOVA decompositions. Uses of the method lead to open problems involving
Online Learning with Kernels
, 2003
"... Kernel based algorithms such as support vector machines have achieved considerable success in various problems in the batch setting where all of the training data is available in advance. Support vector machines combine the socalled kernel trick with the large margin idea. There has been little u ..."
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Cited by 2831 (123 self)
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Kernel based algorithms such as support vector machines have achieved considerable success in various problems in the batch setting where all of the training data is available in advance. Support vector machines combine the socalled kernel trick with the large margin idea. There has been little
KernelBased Object Tracking
, 2003
"... A new approach toward target representation and localization, the central component in visual tracking of nonrigid objects, is proposed. The feature histogram based target representations are regularized by spatial masking with an isotropic kernel. The masking induces spatiallysmooth similarity fu ..."
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Cited by 900 (4 self)
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A new approach toward target representation and localization, the central component in visual tracking of nonrigid objects, is proposed. The feature histogram based target representations are regularized by spatial masking with an isotropic kernel. The masking induces spatiallysmooth similarity
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 537 (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.
Learning the Kernel Matrix with SemiDefinite Programming
, 2002
"... Kernelbased learning algorithms work by embedding the data into a Euclidean space, and then searching for linear relations among the embedded data points. The embedding is performed implicitly, by specifying the inner products between each pair of points in the embedding space. This information ..."
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Cited by 775 (21 self)
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problems in machine learning. In this paper we show how the kernel matrix can be learned from data via semidefinite programming (SDP) techniques. When applied
On the algorithmic implementation of multiclass kernelbased vector machines
 Journal of Machine Learning Research
"... In this paper we describe the algorithmic implementation of multiclass kernelbased vector machines. Our starting point is a generalized notion of the margin to multiclass problems. Using this notion we cast multiclass categorization problems as a constrained optimization problem with a quadratic ob ..."
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Cited by 559 (13 self)
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In this paper we describe the algorithmic implementation of multiclass kernelbased vector machines. Our starting point is a generalized notion of the margin to multiclass problems. Using this notion we cast multiclass categorization problems as a constrained optimization problem with a quadratic
Improved Approximation Algorithms for Maximum Cut and Satisfiability Problems Using Semidefinite Programming
 Journal of the ACM
, 1995
"... We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least .87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds the solution ..."
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Cited by 1211 (13 self)
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the solution to a nonlinear programming relaxation. This relaxation can be interpreted both as a semidefinite program and as an eigenvalue minimization problem. The best previously known approximation algorithms for these problems had performance guarantees of ...
Consensus Problems in Networks of Agents with Switching Topology and TimeDelays
, 2003
"... In this paper, we discuss consensus problems for a network of dynamic agents with fixed and switching topologies. We analyze three cases: i) networks with switching topology and no timedelays, ii) networks with fixed topology and communication timedelays, and iii) maxconsensus problems (or leader ..."
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Cited by 1112 (21 self)
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In this paper, we discuss consensus problems for a network of dynamic agents with fixed and switching topologies. We analyze three cases: i) networks with switching topology and no timedelays, ii) networks with fixed topology and communication timedelays, and iii) maxconsensus problems (or
Results 1  10
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16,861