Related papers: K-Dimensional Coding Schemes in Hilbert Spaces

In this paper, we will introduce the concept of a continuous K-biframe for Hilbert spaces and we present various examples of continuous K-biframes. Furthermore, we investigate their characteristics from the perspective of operator theory by…

We study numerical integration of functions depending on an infinite number of variables. We provide lower error bounds for general deterministic linear algorithms and provide matching upper error bounds with the help of suitable multilevel…

We describe a method to perform functional operations on probability distributions of random variables. The method uses reproducing kernel Hilbert space representations of probability distributions, and it is applicable to all operations…

Classifying points in high dimensional spaces is a fundamental geometric problem in machine learning. In this paper, we address classifying points in the $d$-dimensional Hilbert polygonal metric. The Hilbert metric is a generalization of…

These notes provide a self-contained introduction to kernel methods and their geometric foundations in machine learning. Starting from the construction of Hilbert spaces, we develop the theory of positive definite kernels, reproducing…

This paper is a detailed study of finite-dimensional modules defined on bicomplex numbers. A number of results are proved on bicomplex square matrices, linear operators, orthogonal bases, self-adjoint operators and Hilbert spaces, including…

This paper proposes a concise coding of the cells of n-dimensional finite regular grids. It induces a simple, generic and efficient framework for implementing classical digital topology data structures and algorithms. Discrete subsets of…

In this paper, we focus on frames of operators or K-frames on Hilbert spaces in Parseval cases. Since equal-norm tight frames play important roles for robust data transmission, we aim to study this topics on Parseval K-frames. We will show…

Data visualisation helps understanding data represented by multiple variables, also called features, stored in a large matrix where individuals are stored in lines and variable values in columns. These data structures are frequently called…

Much recent work has addressed the solution of a family of partial differential equations by computing the inverse operator map between the input and solution space. Toward this end, we incorporate function-valued reproducing kernel Hilbert…

We introduce a data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system behaves…

A new method to enclose the pseudospectrum via the numerical range of the inverse of a matrix or linear operator is presented. The method is applied to finite-dimensional discretizations of an operator on an infinite-dimensional Hilbert…

Supervised dimensionality reduction has emerged as an important theme in the last decade. Despite the plethora of models and formulations, there is a lack of a simple model which aims to project the set of patterns into a space defined by…

We provide conditions ensuring that the KKT-type conditions characterizes the global optimality for quadratically constrained (possibly nonconvex) quadratic programming QCQP problems in Hilbert spaces. The key property is the convexity of a…

We expand the basic geometric elements of the simplex method to linear programs in locally convex topological vector spaces and provide conditions under which the method converges in value to optimality. This setting generalizes many…

We propose a novel framework for incorporating qualitative data into quantitative models for causal estimation. Previous methods use categorical variables derived from qualitative data to build quantitative models. However, this approach…

Data vectors are obtained from multiple domains. They are feature vectors of images or vector representations of words. Domains may have different numbers of data vectors with different dimensions. These data vectors from multiple domains…

In this paper we combine the theory of reproducing kernel Hilbert spaces with the field of collocation methods to solve boundary value problems with special emphasis on reproducing property of kernels. From the reproducing property of…

We present quadrature schemes to calculate matrices, where the so-called modified Hilbert transformation is involved. These matrices occur as temporal parts of Galerkin finite element discretizations of parabolic or hyperbolic problems when…

We study two subspace systems in a separable infinite-dimensional Hilbert space up to (bounded) isomorphism. One of the main result of this paper is the following: Isomorphism classes of two subspace systems given by graphs of bounded…