相关论文: Kernel-Cokernel Sequence for Composition and its A…
In this paper, we illustrate the effectiveness of reproducing kernel Hilbert space techniques in the study of composition operators. For weighted Hardy spaces on the unit disk, we characterize the composition operators whose adjoint is…
This article gives a new insight of kernel-based (approximation) methods to solve the high-dimensional stochastic partial differential equations. We will combine the techniques of meshfree approximation and kriging interpolation to extend…
The success of kernel methods has initiated the design of novel positive semidefinite functions, in particular for structured data. A leading design paradigm for this is the convolution kernel, which decomposes structured objects into their…
We address the estimation of "extreme" conditional quantiles i.e. when their order converges to one as the sample size increases. Conditions on the rate of convergence of their order to one are provided to obtain asymptotically Gaussian…
Graph kernels have become an established and widely-used technique for solving classification tasks on graphs. This survey gives a comprehensive overview of techniques for kernel-based graph classification developed in the past 15 years. We…
In this paper, we formulate a new generalized reference kernel hoping to improve the original base kernel using a set of reference vectors. Depending on the selected reference vectors, our formulation shows similarities to approximate…
In this work we consider the problem of learning a positive semidefinite kernel matrix from relative comparisons of the form: "object A is more similar to object B than it is to C", where comparisons are given by humans. Existing solutions…
We prove a coherence theorem for actions of groups on monoidal categories. As an application we prove coherence for arbitrary braided $G$-crossed categories.
In this paper, a fractional version of the Clifford-Fourier transform is introduced, depending on two numerical parameters. A series expansion for the kernel of the resulting integral transform is derived. In the case of even dimension,…
In many instances one has to deal with parametric models. Such models in vector spaces are connected to a linear map. The reproducing kernel Hilbert space and affine- / linear- representations in terms of tensor products are directly…
In this paper, we study a class of multilinear fractional integral operators which have correlation kernels $\prod_{1\leq i<j \leq k}|x_i-x_j|^{-\alpha_{ij}}$. The necessary and sufficient conditions are obtained under which these oprators…
Kernel methods have been widely applied to machine learning and other questions of approximating an unknown function from its finite sample data. To ensure arbitrary accuracy of such approximation, various denseness conditions are imposed…
Kernel-based learning algorithms are widely used in machine learning for problems that make use of the similarity between object pairs. Such algorithms first embed all data points into an alternative space, where the inner product between…
In this article, we present an $O(N \log N)$ rapidly convergent algorithm for the numerical approximation of the convolution integral with radially symmetric weakly singular kernels and compactly supported densities. To achieve the reduced…
A family of general Master theorems for analytic integration over the real (or imaginary) axis with various reciprocal hyperbolic (trig) kernels ($\sinh and/or \cosh$) with varying arguments is developed. Several examples involving…
Properties of relative traces and symmetrizing forms on chains of cyclotomic and affine Hecke algebras are studied. The study relies on a use of bases of these algebras which generalize a normal form for elements of the complex reflection…
It is shown that the property of being bounded below (having closed range) of weighted composition operators on Hardy and Bergman spaces can be tested by their action on a set of simple test functions, including reproducing kernels. The…
We consider sequences of absolute and relative homology and cohomology groups that arise naturally for a filtered cell complex. We establish algebraic relationships between their persistence modules, and show that they contain equivalent…
We study representations of positive definite kernels $K$ in a general setting, but with view to applications to harmonic analysis, to metric geometry, and to realizations of certain stochastic processes. Our initial results are stated for…
This paper deals with the kernel-based approximation of a multivariate periodic function by interpolation at the points of an integration lattice -- a setting that, as pointed out by Zeng, Leung, Hickernell (MCQMC2004, 2006) and Zeng,…