Displaying similar documents to “Inequalities for differentiable reproducing kernels and an application to positive integral operators.”

A kernel-based learning algorithm combining kernel discriminant coordinates and kernel principal components

Karol Deręgowski, Mirosław Krzyśko (2014)

Biometrical Letters

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Kernel principal components (KPC) and kernel discriminant coordinates (KDC), which are the extensions of principal components and discriminant coordinates, respectively, from a linear domain to a nonlinear domain via the kernel trick, are two very popular nonlinear feature extraction methods. The kernel discriminant coordinates space has proven to be a very powerful space for pattern recognition. However, further study shows that there are still drawbacks in this method. To improve the...

Remarks on optimum kernels and optimum boundary kernels

Jitka Poměnková (2008)

Applications of Mathematics

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Kernel smoothers belong to the most popular nonparametric functional estimates used for describing data structure. They can be applied to the fix design regression model as well as to the random design regression model. The main idea of this paper is to present a construction of the optimum kernel and optimum boundary kernel by means of the Gegenbauer and Legendre polynomials.

Self-adjoint differential vector-operators and matrix Hilbert spaces I

Maksim Sokolov (2005)

Open Mathematics

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In the current work a generalization of the famous Weyl-Kodaira inversion formulas for the case of self-adjoint differential vector-operators is proved. A formula for spectral resolutions over an analytical defining set of solutions is discussed. The article is the first part of the planned two-part survey on the structural spectral theory of self-adjoint differential vector-operators in matrix Hilbert spaces.