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Kernel Methods for Clustering [PDF]
Kernel Methods are algorithms that implicitly perform, by replacing the inner product with an appropriate Mercer Kernel, a nonlinear mapping of the input data to a high dimensional Feature Space. In this paper, we describe a Kernel Method for clustering.
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2009
Support vector machines and kernel-based learning methods have been successful in a wide variety of applications, especially for problems in high dimensional input spaces. In this chapter we briefly outline kernel-based learning methods in relation to support vector machines and least squares support vector machines for supervised and unsupervised ...
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Support vector machines and kernel-based learning methods have been successful in a wide variety of applications, especially for problems in high dimensional input spaces. In this chapter we briefly outline kernel-based learning methods in relation to support vector machines and least squares support vector machines for supervised and unsupervised ...
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A reliable data-based bandwidth selection method for kernel density estimation
, 1991We present a new method for data-based selection of the bandwidth in kernel density estimation which has excellent properties. It improves on a recent procedure of Park and Marron (which itself is a good method) in various ways. First, the new method has
S. Sheather, M. C. Jones
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The Reproducing Kernel Method. II
Journal of Mathematical Physics, 1972The explicit solution of the Cauchy problem ∂N/∂t = HN by means of reproducing kernels is obtained under various forms: conformal mapping expansions, Sheffer polynomial expansion, polynomials orthogonal on a family of curves; the convergence is studied for both Szegö and Bergman kernels.
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A High-Order Kernel Method for Diffusion and Reaction-Diffusion Equations on Surfaces
Journal of Scientific Computing, 2012In this paper we present a high-order kernel method for numerically solving diffusion and reaction-diffusion partial differential equations (PDEs) on smooth, closed surfaces embedded in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage ...
E. Fuselier, G. Wright
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IEEE Transactions on Pattern Analysis and Machine Intelligence, 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.
D. Comaniciu+2 more
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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.
D. Comaniciu+2 more
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2007
During the past decade, a major revolution has taken place in pattern-recognition technology with the introduction of rigorous and powerful mathematical approaches in problem domains previously treated with heuristic and less efficient techniques.
Cristianini, N.+2 more
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During the past decade, a major revolution has taken place in pattern-recognition technology with the introduction of rigorous and powerful mathematical approaches in problem domains previously treated with heuristic and less efficient techniques.
Cristianini, N.+2 more
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2013
The kernel method was originally invented in Aizerman et al. (Autom. Remote Control, 25, 821–837, 1964). The key idea is to project the training set in a lower-dimensional space into a high-dimensional kernel (feature) space by means of a set of nonlinear kernel functions.
Ke-Lin Du, Mallappa Kumara Swamy
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The kernel method was originally invented in Aizerman et al. (Autom. Remote Control, 25, 821–837, 1964). The key idea is to project the training set in a lower-dimensional space into a high-dimensional kernel (feature) space by means of a set of nonlinear kernel functions.
Ke-Lin Du, Mallappa Kumara Swamy
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Reproducing kernel particle methods
International Journal for Numerical Methods in Fluids, 1995AbstractA new continuous reproducing kernel interpolation function which explores the attractive features of the flexible time‐frequency and space‐wave number localization of a window function is developed. This method is motivated by the theory of wavelets and also has the desirable attributes of the recently proposed smooth particle hydrodynamics ...
Wing Kam Liu, Sukky Jun, Yi Fei Zhang
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Kernel Methods in Bioinformatics
2011Kernel methods have now witnessed more than a decade of increasing popularity in the bioinformatics community. In this article, we will compactly review this development, examining the areas in which kernel methods have contributed to computational biology and describing the reasons for their success.
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