This article studies the distributed parameter system that governs adaptive estimation by mobile sensor networks of external fields in a reproducing kernel Hilbert space (RKHS). The begins with derivation conditions guarantee well-posedness ideal, infinite dimensional governing equations evolution for centralized scheme. Subsequently, convergence finite approximations is studied. Rates all form...

In this paper we provide a representer theorem for a concatenation of (linear combinations of) kernel functions of reproducing kernel Hilbert spaces. This fundamental result serves as a first mathematical foundation for the analysis of machine learning algorithms based on compositions of functions. As a direct consequence of this new representer theorem, the corresponding infinite-dimensional m...

A reproducing-kernel Hilbert space approach to image interpolation is introduced. In particular, the reproducing kernels of Sobolev spaces are shown to be exponential functions. These functions, in turn, give rise to alternative interpolation kernels that outperform presently available designs. Both theoretical and experimental results are presented.

We focus on covariance criteria for finding a suitable subspace for regression in a reproducing kernel Hilbert space: kernel principal component analysis, kernel partial least squares and kernel canonical correlation analysis, and we demonstrate how this fits within a more general context of subspace regression. For the kernel partial least squares case some variants are considered and the meth...

The operator-valued Schur-class is defined to be the set of holomorphic functions S mapping the unit disk into the space of contraction operators between two Hilbert spaces. There are a number of alternate characterizations: the operator of multiplication by S defines a contraction operator between two Hardy Hilbert spaces, S satisfies a von Neumann inequality, a certain operator-valued kernel ...

In this paper, we study an online learning algorithm in Reproducing Kernel Hilbert Spaces (RKHS) and general Hilbert spaces. We present a general form of the stochastic gradient method to minimize a quadratic potential function by an independent identically distributed (i.i.d.) sample sequence, and show a probabilistic upper bound for its convergence.

A reproducing-kernel Hilbert space approach to image interpolation is introduced. In particular, the reproducing kernels of Sobolev spaces are shown to be exponential functions. These functions, in turn, give rise to alternative interpolation kernels that outperform presently available designs. Both theoretical and experimental results are presented.

We study the stability properties of nonlinear multi-task regression in reproducing Hilbert spaces with operator-valued kernels. Such kernels, a.k.a. multi-task kernels, are appropriate for learning problems with nonscalar outputs like multi-task learning and structured output prediction. We show that multi-task kernel regression algorithms are uniformly stable in the general case of infinite-d...

We propose a framework for semi-supervised learning in reproducing kernel Hilbert spaces using local invariances that explicitly characterize the behavior of the target function around both labeled and unlabeled data instances. Such invariances include: invariance to small changes to the data instances, invariance to averaging across a small neighbourhood around data instances, and invariance t...

In order to use the method of(least squares) collocation for the computation o f an approximation to the anomalous potential o f the Earth (T) it is necessary to specify a reproducing kernel Hilbert space the dual o.f which contain the (linear) functionals associated with the observation~ The specification includes the prescription o f an inner product or an equivalent norrrL It is demonstrated...