Related papers: K-Dimensional Coding Schemes in Hilbert Spaces

Insightful visualization of multidimensional scalar fields, in particular parameter spaces, is key to many fields in computational science and engineering. We propose a principal component-based approach to visualize such fields that…

This paper is concerned with the numerical minimization of energy functionals in Hilbert spaces involving convex constraints coinciding with a semi-norm for a subspace. The optimization is realized by alternating minimizations of the…

Theoretical studies have proven that the Hilbert space has remarkable performance in many fields of applications. Frames in tensor product of Hilbert spaces were introduced to generalize the inner product to high-order tensors. However,…

K-frames are strongly tools for the reconstruction elements from the range of a bounded linear operator K on a separable Hilbert space H. In this paper, we study some properties of K-frames and introduce the K-frame multipliers. We also…

In this paper, we introduce a new concept of K-biframes for Hilbert spaces. We then examine several characterizations with the assistance of a biframe operator. Moreover, we investigate their properties from the perspective of operator…

K-frames, a new generalization of frames, were recently considered by L. Gavruta in connection with atomic systems and some problems arising in sampling theory. Also, fusion frames are an important generalization of frames, applied in a…

In this paper, we consider regression models with a Hilbert-space-valued predictor and a scalar response, where the response depends on the predictor only through a finite number of projections. The linear subspace spanned by these…

Space-filling curves like the Hilbert-curve, Peano-curve and Z-order map natural or real numbers from a two or higher dimensional space to a one dimensional space preserving locality. They have numerous applications like search structures,…

By introducing Hilbert space and operators, we show how probabilities, approximations and entropy encoding from signal and image processing allow precise formulas and quantitative estimates. Our main results yield orthogonal bases which…

We implement an all-optical setup demonstrating kernel-based quantum machine learning for two-dimensional classification problems. In this hybrid approach, kernel evaluations are outsourced to projective measurements on suitably designed…

We show that any decoherence functional $D$ can be represented by a spanning vector-valued measure on a complex Hilbert space. Moreover, this representation is unique up to an isomorphism when the system is finite. We consider the natural…

The basic idea of quantum computing is surprisingly similar to that of kernel methods in machine learning, namely to efficiently perform computations in an intractably large Hilbert space. In this paper we explore some theoretical…

In a general context of positive definite kernels $k$, we develop tools and algorithms for sampling in reproducing kernel Hilbert space $\mathscr{H}$ (RKHS). With reference to these RKHSs, our results allow inference from samples; more…

In this article a unified approach to iterative soft-thresholding algorithms for the solution of linear operator equations in infinite dimensional Hilbert spaces is presented. We formulate the algorithm in the framework of generalized…

We introduce a novel 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…

We propose a new random sketching approach for embedding high-dimensional Hilbert-Schmidt operators, using random input-output pairs. Such operator can then be approximated in a low-dimensional subspace of operators by solving a small…

Finite plane geometry is associated with finite dimensional Hilbert space. The association allows mapping of q-number Hilbert space observables to the c-number formalism of quantum mechanics in phase space. The mapped entities reflect…

Useful relations describing arbitrary parameters of given quantum systems can be derived from simple physical constraints imposed on the vectors in the corresponding Hilbert space. This is well known and it usually proceeds by partitioning…

We provide a detailed description of the model Hilbert space $L^2(\bbR; d\Sigma; \cK)$, were $\cK$ represents a complex, separable Hilbert space, and $\Sigma$ denotes a bounded operator-valued measure. In particular, we show that several…

Efficient methods for encoding and compression are likely to pave way towards the problem of efficient trainability on higher dimensional Hilbert spaces overcoming issues of barren plateaus. Here we propose an alternative approach to…