Journal ArticleDOI
Vector valued reproducing kernel hilbert spaces of integrable functions and mercer theorem
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In this paper, the authors characterize the reproducing kernel Hilbert spaces whose elements are p-integrable functions in terms of the boundedness of the integral operator whose kernel is the Reproducing Kernel.Abstract:
We characterize the reproducing kernel Hilbert spaces whose elements are p-integrable functions in terms of the boundedness of the integral operator whose kernel is the reproducing kernel. Moreover, for p = 2, we show that the spectral decomposition of this integral operator gives a complete description of the reproducing kernel, extending the Mercer theorem.read more
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Optimal Rates for the Regularized Least-Squares Algorithm
Andrea Caponnetto,E. De Vito +1 more
TL;DR: A complete minimax analysis of the problem is described, showing that the convergence rates obtained by regularized least-squares estimators are indeed optimal over a suitable class of priors defined by the considered kernel.
Journal ArticleDOI
Survey Kernel methods in system identification, machine learning and function estimation: A survey
TL;DR: A survey of kernel-based regularization and its connections with reproducing kernel Hilbert spaces and Bayesian estimation of Gaussian processes to demonstrate that learning techniques tailored to the specific features of dynamic systems may outperform conventional parametric approaches for identification of stable linear systems.
Book
Kernels for Vector-Valued Functions: A Review
TL;DR: This monograph reviews different methods to design or learn valid kernel functions for multiple outputs, paying particular attention to the connection between probabilistic and functional methods.
Journal ArticleDOI
Robust Point Matching via Vector Field Consensus
TL;DR: This paper proposes an efficient algorithm, called vector field consensus, for establishing robust point correspondences between two sets of points, and suggests a two-stage strategy, where the nonparametric model is used to reduce the size of the putative set and a parametric variant of the approach to estimate the geometric parameters.
Journal ArticleDOI
Robust Feature Matching for Remote Sensing Image Registration via Locally Linear Transforming
TL;DR: This paper proposes a flexible and general algorithm, which is called locally linear transforming (LLT), for both rigid and nonrigid feature matching of remote sensing images, which outperforms current state-of-the-art methods, particularly in the case of severe outliers.
References
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Book
Ten lectures on wavelets
TL;DR: This paper presents a meta-analyses of the wavelet transforms of Coxeter’s inequality and its applications to multiresolutional analysis and orthonormal bases.
Journal ArticleDOI
Ten Lectures on Wavelets
TL;DR: In this article, the regularity of compactly supported wavelets and symmetry of wavelet bases are discussed. But the authors focus on the orthonormal bases of wavelets, rather than the continuous wavelet transform.
Journal ArticleDOI
Theory of Reproducing Kernels.
TL;DR: In this paper, a short historical introduction is given to indicate the different manners in which these kernels have been used by various investigators and discuss the more important trends of the application of these kernels without attempting, however, a complete bibliography of the subject matter.
Book
A Course in Functional Analysis
TL;DR: In this article, an introductory text in functional analysis aimed at the graduate student with a firm background in integration and measure theory is presented, which helps the student to develop an intuitive feel for the subject.
Journal ArticleDOI
On the mathematical foundations of learning
TL;DR: A main theme of this report is the relationship of approximation to learning and the primary role of sampling (inductive inference) and relations of the theory of learning to the mainstream of mathematics are emphasized.