منابع مشابه
F ¨ Ur Mathematik in Den Naturwissenschaften Leipzig Power Series Kernels Power Series Kernels
We introduce a class of analytic positive definite multivariate kernels which includes infinite dot product kernels as sometimes used in machine learning, certain new nonlinearly factorizable kernels and a kernel which is closely related to the Gaussian. Each such kernel reproduces in a certain 'native' Hilbert space of multivariate analytic functions. If functions from this space are interpola...
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Let 9 be a connected complex domain and let G be a group of holomorphic transformations of 9. Let Hi (i = 1,2) be reproducing kernel Hilbert spaces of holomorphic functions from 9 to finite dimensional complex vector spaces Vi such that each Hi carries a unitary representation Vi of G. Then U1 @ Us is unitary in a reproducing kernel Hilbert space of holomorphic functions from 5-3 X 9 to Vi @ V,...
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Let M = M̃/Γ be a Kähler manifold, where Γ ' π1(M) and where M̃ is the universal Kähler cover. Let (L, h) → M be a positive Hermitian holomorophic line bundle. We first prove that the L Szegő projector Π̃N for L holomorphic sections on the lifted bundle L̃ → M̃ is related to the Szegő projector for H(M,L ) by Π̂N (x, y) = ∑ γ∈Γ ̃̂ ΠN (γ · x, y). We apply this result to give a simple proof of Napier’s t...
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We deduce decay rates for eigenvalues of integral operators generated by power serieslike kernels on a subset X of either Rq or Cq . A power series-like kernel is a Mercer kernel having a series expansion based on an orthogonal family { fα}α∈Zq+ in L 2(X ,μ) , in which μ is a complete measure on X . As so, we show that the eigenvalues of the integral operators are given by an explicit formula d...
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Time series analysis is an important and complex problem in machine learning and statistics. Real-world applications can consist of very large and high dimensional time series data. Support Vector Machines (SVMs) are a popular tool for the analysis of such data sets. This paper presents some SVM kernel functions and disusses their relative merits, depending on the type of data that is used.
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ژورنال
عنوان ژورنال: Constructive Approximation
سال: 2008
ISSN: 0176-4276,1432-0940
DOI: 10.1007/s00365-008-9012-4