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On discrete analytic functions: Products, Rational Functions, and some Associated Reproducing Kernel Hilbert Spaces. ArXiv eprints
, 2012
"... ar ..."
Sparseness of support vector machines
, 2003
"... Support vector machines (SVMs) construct decision functions that are linear combinations of kernel evaluations on the training set. The samples with nonvanishing coefficients are called support vectors. In this work we establish lower (asymptotical) bounds on the number of support vectors. On our w ..."
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Cited by 263 (35 self)
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in the associated reproducing kernel Hilbert 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 510 (0 self)
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the theory of infinitely divisible positive definite functions. Fundamentals of this theory and the theory of reproducing kernel Hilbert spaces are reviewed and applied in establishing the validity of the method.
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 2807 (126 self)
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use of these methods in an online setting suitable for realtime applications. In this paper we consider online learning in a Reproducing Kernel Hilbert Space. By considering classical stochastic gradient descent within a feature space, and the use of some straightforward tricks, we develop simple
Kernel independent component analysis
 Journal of Machine Learning Research
, 2002
"... We present a class of algorithms for independent component analysis (ICA) which use contrast functions based on canonical correlations in a reproducing kernel Hilbert space. On the one hand, we show that our contrast functions are related to mutual information and have desirable mathematical propert ..."
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Cited by 465 (27 self)
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We present a class of algorithms for independent component analysis (ICA) which use contrast functions based on canonical correlations in a reproducing kernel Hilbert space. On the one hand, we show that our contrast functions are related to mutual information and have desirable mathematical
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 780 (22 self)
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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
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 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
Fisher Discriminant Analysis With Kernels
, 1999
"... A nonlinear classification technique based on Fisher's discriminant is proposed. The main ingredient is the kernel trick which allows the efficient computation of Fisher discriminant in feature space. The linear classification in feature space corresponds to a (powerful) nonlinear decision f ..."
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Cited by 493 (18 self)
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A nonlinear classification technique based on Fisher's discriminant is proposed. The main ingredient is the kernel trick which allows the efficient computation of Fisher discriminant in feature space. The linear classification in feature space corresponds to a (powerful) nonlinear decision
The xKernel: An Architecture for Implementing Network Protocols
 IEEE Transactions on Software Engineering
, 1991
"... This paper describes a new operating system kernel, called the xkernel, that provides an explicit architecture for constructing and composing network protocols. Our experience implementing and evaluating several protocols in the xkernel shows that this architecture is both general enough to acc ..."
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Cited by 663 (21 self)
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This paper describes a new operating system kernel, called the xkernel, that provides an explicit architecture for constructing and composing network protocols. Our experience implementing and evaluating several protocols in the xkernel shows that this architecture is both general enough
REPRODUCING KERNEL HILBERT SPACES
, 2004
"... We reformulate the original componentbycomponent algorithm for rank1 lattices in a matrixvector notation so as to highlight its structural properties. For function spaces similar to a weighted Korobov space, we derive a technique which has construction cost O(sn log(n)), in contrast with the ori ..."
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We reformulate the original componentbycomponent algorithm for rank1 lattices in a matrixvector notation so as to highlight its structural properties. For function spaces similar to a weighted Korobov space, we derive a technique which has construction cost O(sn log(n)), in contrast
Results 1  10
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810,424