Related papers: Matrix-valued Kernels for Shape Deformation Analys…

We consider conditions on a given system $\mathcal{F}$ of vectors in Hilbert space $\mathcal{H}$, forming a frame, which turn $\mathcal{H}$ into a reproducing kernel Hilbert space. It is assumed that the vectors in $\mathcal{F}$ are…

Implicit neural representations (INRs), which leverage neural networks to represent signals by mapping coordinates to their corresponding attributes, have garnered significant attention. They are extensively utilized for image…

In Magnetic Resonance Imaging (MRI) data samples are collected in the spatial frequency domain (k-space), typically by time-consuming line-by-line scanning on a Cartesian grid. Scans can be accelerated by simultaneous acquisition of data…

Neural implicit functions have achieved impressive results for reconstructing 3D shapes from single images. However, the image features for describing 3D point samplings of implicit functions are less effective when significant variations…

We introduce and study a class $\mathcal{M}$ of generalized positive definite kernels of the form $K\colon X\times X\to L(\mathfrak{A},L(H))$, where $\mathfrak{A}$ is a unital $C^{*}$-algebra and $H$ a Hilbert space. These kernels encode…

Reproducing kernel Hilbert spaces (RKHSs) are special Hilbert spaces where all the evaluation functionals are linear and bounded. They are in one-to-one correspondence with positive definite maps called kernels. Stable RKHSs enjoy the…

This manuscript presents an algorithm for obtaining an approximation of a nonlinear high order control affine dynamical system. Controlled trajectories of the system are leveraged as the central unit of information via embedding them in…

We present new classes of positive definite kernels on non-standard spaces that are integrally strictly positive definite or characteristic. In particular, we discuss radial kernels on separable Hilbert spaces, and introduce broad classes…

In this paper we study hermitian kernels invariant under the action of a semigroup with involution. We characterize those hermitian kernels which realize the given action by bounded operators on a Krein space. Applications to the GNS…

The aim of the paper is to create a link between the theory of reproducing kernel Hilbert spaces (RKHS) and the notion of a unitary representation of a group or of a groupoid. More specifically, it is demonstrated on one hand, how to…

The kernel trick concept, formulated as an inner product in a feature space, facilitates powerful extensions to many well-known algorithms. While the kernel matrix involves inner products in the feature space, the sample covariance matrix…

Nonlinear kernel regression models are often used in statistics and machine learning because they are more accurate than linear models. Variable selection for kernel regression models is a challenge partly because, unlike the linear…

Multiscale Models are known to be successful in uncovering and analyzing the structures in data at different resolutions. In the current work we propose a feature driven Reproducing Kernel Hilbert space (RKHS), for which the associated…

For a bounded domain $D \subset \mathbb{C}^n$, let $K_D = K_D(z) > 0$ denote the Bergman kernel on the diagonal and consider the reproducing kernel Hilbert space of holomorphic functions on $D$ that are square integrable with respect to the…

We develop a mathematical framework to address a broad class of metric and preference learning problems within a Hilbert space. We obtain a novel representer theorem for the simultaneous task of metric and preference learning. Our key…

The geometric approach to diffeomorphic image registration known as "large deformation by diffeomorphic metric mapping" (LDDMM) is based on a left action of diffeomorphisms on images, and a right-invariant metric on a diffeomorphism group,…

In this paper, we use the infamous continuous and nowhere differentiable Weierstrass function as a prototype to define a Weierstrass fractal kernel. We investigate the properties of the reproducing kernel Hilbert space (RKHS) associated…

Any applied mathematical model contains parameters. The paper proposes to use kernel learning for the parametric analysis of the model. The approach consists in setting a distribution on the parameter space, obtaining a finite training…

Metric learning for classification has been intensively studied over the last decade. The idea is to learn a metric space induced from a normed vector space on which data from different classes are well separated. Different measures of the…

Many scientific problems involve data exhibiting both temporal and cross-sectional dependencies. While linear dependencies have been extensively studied, the theoretical analysis of regression estimators under nonlinear dependencies remains…