Related papers: On Orthogonal Projections on the Space of Consiste…
A recursive approach for shrinking coefficients of an atomic decomposition is proposed. The corresponding algorithm evolves so as to provide at each iteration a) the orthogonal projection of a signal onto a reduced subspace and b) the index…
We examine a class of embeddings based on structured random matrices with orthogonal rows which can be applied in many machine learning applications including dimensionality reduction and kernel approximation. For both the…
With the growth of magnitude of multi-agent networks, distributed optimization holds considerable significance within complex systems. Convergence, a pivotal goal in this domain, is contingent upon the analysis of infinite products of…
The inhomogeneous metric theory for the set of simultaneously $\psi$-approximable points lying on a planar curve is developed. Our results naturally incorporate the homogeneous Khintchine-Jarnik type theorems recently established in [Ann.…
Generalized Fourier series with orthogonal polynomial bases have useful applications in several fields, including differential equations, pattern recognition, and image and signal processing. However, computing the generalized Fourier…
In this paper, we propose an efficient and scalable low rank matrix completion algorithm. The key idea is to extend orthogonal matching pursuit method from the vector case to the matrix case. We further propose an economic version of our…
In this paper we consider the collaborative ranking setting: a pool of users each provides a small number of pairwise preferences between $d$ possible items; from these we need to predict preferences of the users for items they have not yet…
We present a systematic study on the linear convergence rates of the powers of (real or complex) matrices. We derive a characterization when the optimal convergence rate is attained. This characterization is given in terms of…
Multicriteria Decision Making problems are important both for individuals and groups. Pairwise comparisons have become popular in the theory and practice of preference modelling and quantification. We focus on decision problems where the…
A precision matrix is the inverse of a covariance matrix. In this paper, we study the problem of estimating the precision matrix with a known graphical structure under high-dimensional settings. We propose a simple estimator of the…
Gaussian processes (GPs) defined through intrinsic random fields provide a flexible framework for modeling spatial phenomena, and have been advocated in a variety of applications over the past several decades. Nevertheless, their adoption…
Optimization problems, generalized equations, and the multitude of other variational problems invariably lead to the analysis of sets and set-valued mappings as well as their approximations. We review the central concept of set-convergence…
A matrix-valued inner product was proposed before to construct orthonormal matrix-valued wavelets for matrix-valued signals. It introduces a weaker orthogonality for matrix-valued signals than the orthogonality of all components in a matrix…
An approach is proposed which, given a family of linearly independent functions, constructs the appropriate biorthogonal set so as to represent the orthogonal projector operator onto the corresponding subspace. The procedure evolves…
A nonstandard application of bivariate polynomial interpolation is discussed: the implicitization of a rational algebraic curve given by its parametric equations. Three different approaches using the same interpolation space are considered,…
Subjective assessment tests are often employed to evaluate image processing systems, notably image and video compression, super-resolution among others and have been used as an indisputable way to provide evidence of the performance of an…
The social and economic importance of large bodies of programs and data that are potentially long-lived has attracted much attention in the commercial and research communities. Here we concentrate on a set of methodologies and technologies…
We give a new proof for an equality of certain max-min and min-max approximation problems involving normal matrices. The previously published proofs of this equality apply tools from matrix theory, (analytic) optimization theory and…
Transfer matrices and matrix product operators play an ubiquitous role in the field of many body physics. This paper gives an ideosyncratic overview of applications, exact results and computational aspects of diagonalizing transfer matrices…
This paper introduces an approach for detecting differences in the first-order structures of spatial point patterns. The proposed approach leverages the kernel mean embedding in a novel way by introducing its approximate version tailored to…