Related papers: Sampling with positive definite kernels and an ass…
Most machine learning algorithms, such as classification or regression, treat the individual data point as the object of interest. Here we consider extending machine learning algorithms to operate on groups of data points. We suggest…
The two-sample hypothesis testing problem is studied for the challenging scenario of high dimensional data sets with small sample sizes. We show that the two-sample hypothesis testing problem can be posed as a one-class set classification…
Anomaly detection based on one-class classification algorithms is broadly used in many applied domains like image processing (e.g. detection of whether a patient is "cancerous" or "healthy" from mammography image), network intrusion…
This work presents a nonparametric framework for dissipativity learning in reproducing kernel Hilbert spaces, which enables data-driven certification of stability and performance properties for unknown nonlinear systems without requiring an…
Kernel methods have been among the most popular techniques in machine learning, where learning tasks are solved using the property of reproducing kernel Hilbert space (RKHS). In this paper, we propose a novel data analysis framework with…
We show that sampling or interpolation formulas in reproducing kernel Hilbert spaces can be obtained by reproducing kernels whose dual systems form molecules, ensuring that the size profile of a function is fully reflected by the size…
In this note we prove that the reproducing kernel of a Hilbert space satisfying the division property has integrable form, is locally of trace class, and the Hilbert space itself is a Hilbert space of holomorphic functions.
The aim of this paper is to present a unified framework in the setting of Hilbert $C^*$-modules for the scalar- and vector-valued reproducing kernel Hilbert spaces and $C^*$-valued reproducing kernel spaces. We investigate conditionally…
This paper is devoted to the study of vector valued reproducing kernel Hilbert spaces. We focus on two aspects: vector valued feature maps and universal kernels. In particular we characterize the structure of translation invariant kernels…
This article presents a quantum computing approach to designing of similarity measures and kernels for classification of stochastic symbolic time series. In the area of machine learning, kernels are important components of various…
The accuracy and complexity of kernel learning algorithms is determined by the set of kernels over which it is able to optimize. An ideal set of kernels should: admit a linear parameterization (tractability); be dense in the set of all…
The necessary and sufficient conditions for existence of a generalized representer theorem are presented for learning Hilbert space-valued functions. Representer theorems involving explicit basis functions and Reproducing Kernels are a…
We provide a characterization for the continuous positive definite kernels on $\mathbb R^d$ that are invariant to linear isometries, i.e. invariant under the orthogonal group $O(d)$. Furthermore, we provide necessary and sufficient…
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…
We discuss the structure of positive definite kernels in terms of operator models. In particular, we introduce two models, one of Hessenberg type and another one that we call near triangular. These models produce parametrizations of the…
The composition operators preserving total non-negativity and total positivity for various classes of kernels are classified, following three themes. Letting a function act by post composition on kernels with arbitrary domains, it is shown…
Motivated by the problem of learning with small sample sizes, this paper shows how to incorporate into support-vector machines (SVMs) those properties that have made convolutional neural networks (CNNs) successful. Particularly important is…
The purpose of this work is to explore the existence and properties of reproducing kernel Hilbert subspaces of $L^2(\C, \, d^2z/\pi)$ based on subsets of complex Hermite polynomials. The resulting coherent states (CS) form a family…
Let k be an algebraically closed field of characteristic zero and let B be a finitely generated k-domain. We study semisimple derivations on B, with special emphasis on those whose eigenvalues are integers. For such derivations, after…
We define an extension of operator-valued positive definite functions from the real or complex setting to topological algebras, and describe their associated reproducing kernel spaces. The case of entire functions is of special interest,…