The nature of the classical canonical phase-space variables for gravity suggests that the associated quantum field operators should obey affine commutation relations rather than canonical commutation relations. Prior to the introduction of constraints, a primary kinematical representation is derived in the form of a reproducing kernel and its associated reproducing kernel Hilbert space. Constra...

This paper studies the construction of a refinement kernel for a given operator-valued reproducing kernel such that the vector-valued reproducing kernel Hilbert space of the refinement kernel contains that of the given kernel as a subspace. The study is motivated from the need of updating the current operator-valued reproducing kernel in multi-task learning when underfitting or overfitting occu...

This paper considers the regularized learning algorithm associated with the leastsquare loss and reproducing kernel Hilbert spaces. The target is the error analysis for the regression problem in learning theory. A novel regularization approach is presented, which yields satisfactory learning rates. The rates depend on the approximation property and the capacity of the reproducing kernel Hilbert...

Performance of the linear models, widely used within the framework of adaptive line enhancement (ALE), deteriorates dramatically in the presence of non-Gaussian noises. On the other hand, adaptive implementation of nonlinear models, e.g. the Volterra filters, suffers from the severe problems of large number of parameters and slow convergence. Nonetheless, kernel methods are emerging solutions t...

The reproducing kernel function of a weighted Bergman space over domains in C is known explicitly in only a small number of instances. Here, we introduce a process of orthogonal norm expansion along a subvariety of codimension 1, which also leads to a series expansion of the reproducing kernel in terms of reproducing kernels defined on the subvariety. The problem of finding the reproducing kern...

We consider conditions on a given system F of vectors in Hilbert space H, forming a frame, which turn H into a reproducing kernel Hilbert space. It is assumed that the vectors in F are functions on some set Ω. We then identify conditions on these functions which automatically give H the structure of a reproducing kernel Hilbert space of functions on Ω. We further give an explicit formula for th...

We focus on three methods 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 a least squares support vector machine style der...

Kernel machines are widely considered to be powerful tools in various fields of information science. By using a kernel, an unknown target is represented by a function that belongs to a reproducing kernel Hilbert space (RKHS) corresponding to the kernel. The application area is widened by enlarging the RKHS such that it includes a wide class of functions. In this study, we demonstrate a method t...

of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy NONLINEAR SIGNAL PROCESSING BASED ON REPRODUCING KERNEL HILBERT SPACE By Jianwu Xu December 2007 Chair: Jose C. Principe Major: Electrical and Computer Engineering My research aimed at analyzing the recently proposed correntropy function...